using i64 = long long;
using i128 = __int128;
using u32 = unsigned;
using u64 = unsigned long long;
using f32 = double;
using f64 = long double;
#define uset unordered_set
#define umap unordered_map
#define vi vector<int>
#define vvi vector<vi>
#define vll vector<i64>
#define vvll vector<vll>
#define pii pair<int, int>
#define pll pair<i64, i64>
#define vpii vector<pii>
#define vpll vector<pll>
#define vvpii vector<vpii>
#define vvpll vector<vpll>
#define vz vector<Z>
#define vvz vector<vz>
#define pb push_back
#define pq priority_queue
#define ALL(x) (x).begin(), (x).end()
#define rep(i, x, y) for (int (i) = (x); (i) < (y); (i)++)
#define repr(i, x, y) for (int (i) = (x); (i) > (y); (i)--)
#define YES "YES\n"
#define NO "NO\n"
#define SZ(x) (static_cast<int>(x.size()))
#include <bits/stdc++.h>
using namespace std;
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m`
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned long long y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#if __cplusplus >= 202002L
#include <bit>
#endif
namespace atcoder {
namespace internal {
#if __cplusplus >= 202002L
using std::bit_ceil;
#else
// @return same with std::bit::bit_ceil
unsigned int bit_ceil(unsigned int n) {
unsigned int x = 1;
while (x < (unsigned int)(n)) x *= 2;
return x;
}
#endif
// @param n `1 <= n`
// @return same with std::bit::countr_zero
int countr_zero(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
// @param n `1 <= n`
// @return same with std::bit::countr_zero
constexpr int countr_zero_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
template <class E> struct csr {
std::vector<int> start;
std::vector<E> elist;
explicit csr(int n, const std::vector<std::pair<int, E>>& edges)
: start(n + 1), elist(edges.size()) {
for (auto e : edges) {
start[e.first + 1]++;
}
for (int i = 1; i <= n; i++) {
start[i] += start[i - 1];
}
auto counter = start;
for (auto e : edges) {
elist[counter[e.first]++] = e.second;
}
}
};
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
template <class T> struct simple_queue {
std::vector<T> payload;
int pos = 0;
void reserve(int n) { payload.reserve(n); }
int size() const { return int(payload.size()) - pos; }
bool empty() const { return pos == int(payload.size()); }
void push(const T& t) { payload.push_back(t); }
T& front() { return payload[pos]; }
void clear() {
payload.clear();
pos = 0;
}
void pop() { pos++; }
};
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
// Reference:
// R. Tarjan,
// Depth-First Search and Linear Graph Algorithms
struct scc_graph {
public:
explicit scc_graph(int n) : _n(n) {}
int num_vertices() { return _n; }
void add_edge(int from, int to) { edges.push_back({from, {to}}); }
// @return pair of (# of scc, scc id)
std::pair<int, std::vector<int>> scc_ids() {
auto g = csr<edge>(_n, edges);
int now_ord = 0, group_num = 0;
std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
visited.reserve(_n);
auto dfs = [&](auto self, int v) -> void {
low[v] = ord[v] = now_ord++;
visited.push_back(v);
for (int i = g.start[v]; i < g.start[v + 1]; i++) {
auto to = g.elist[i].to;
if (ord[to] == -1) {
self(self, to);
low[v] = std::min(low[v], low[to]);
} else {
low[v] = std::min(low[v], ord[to]);
}
}
if (low[v] == ord[v]) {
while (true) {
int u = visited.back();
visited.pop_back();
ord[u] = _n;
ids[u] = group_num;
if (u == v) break;
}
group_num++;
}
};
for (int i = 0; i < _n; i++) {
if (ord[i] == -1) dfs(dfs, i);
}
for (auto& x : ids) {
x = group_num - 1 - x;
}
return {group_num, ids};
}
std::vector<std::vector<int>> scc() {
auto ids = scc_ids();
int group_num = ids.first;
std::vector<int> counts(group_num);
for (auto x : ids.second) counts[x]++;
std::vector<std::vector<int>> groups(ids.first);
for (int i = 0; i < group_num; i++) {
groups[i].reserve(counts[i]);
}
for (int i = 0; i < _n; i++) {
groups[ids.second[i]].push_back(i);
}
return groups;
}
private:
int _n;
struct edge {
int to;
};
std::vector<std::pair<int, edge>> edges;
};
} // namespace internal
} // namespace atcoder
mt19937_64 rng((unsigned) chrono::high_resolution_clock::now().time_since_epoch().count());
template<typename _Tp = int, unsigned load1 = 200,unsigned load2 = 64>
struct sortedlistPlus{
using Iterator = vector<_Tp>::iterator;
const unsigned load1X = load1 * 2, lg1 = __lg(load1X);
const unsigned load2X = load2 * 2, lg2 = __lg(load2X);
const _Tp minVal = std::numeric_limits<_Tp>::min();
vector<vector<_Tp>> blocks;
vector<int> bitCnt;
vector<_Tp> blkMax;
vector<_Tp> segMax;
vector<_Tp> segSize;
int elementCnt;
sortedlistPlus(){ clear();}
sortedlistPlus(vector<_Tp> A){
ranges::sort(A);
elementCnt = A.size();
blocks.reserve(elementCnt / load1 + 2);
blocks.resize(1);
for(int l = 0 ; l < elementCnt; l += load1)
blocks.emplace_back(A.data() + l , A.data() + min<int>(l + load1, elementCnt));
_expand();
}
void clear(){
blocks.resize(1);
bitCnt.resize(1);
blkMax.resize(1);
segMax.clear(), segSize.clear();
elementCnt = 0;
}
void chmax(_Tp& a, auto&& b){ if(b > a) a = b;}
pair<int, Iterator> _lower_bound(_Tp x){
if(segSize.empty()) return {0, blocks[0].end()};
int l = -1 , r = segSize.size() - 1 , mid;
while(r - l > 1) if(segMax[mid=l+r>>1]>=x) r = mid; else l = mid;
l = r<<lg2|0;
r = r<<lg2|segSize[r];
while(r - l > 1) if(blkMax[mid=l+r>>1]>=x) r = mid; else l = mid;
return pair{r, (Iterator)ranges::lower_bound(blocks[r],x)};
}
pair<int, Iterator> _upper_bound(_Tp x){
if(segSize.empty()) return {0, blocks[0].end()};
int l = -1 , r = segSize.size() - 1 , mid;
while(r - l > 1) if(segMax[mid=l+r>>1]>x) r = mid; else l = mid;
l = r<<lg2|0;
r = r<<lg2|segSize[r];
while(r - l > 1) if(blkMax[mid=l+r>>1]>x) r = mid; else l = mid;
return pair{r, (Iterator)ranges::upper_bound(blocks[r],x)};
}
void _rangeBitModify(int b1, int b2){
fill(bitCnt.data() + b1, bitCnt.data() + b2 + 1, 0);
for(int i = b1 ; i <= b2; ++i){
if(blocks[i].size()) {
bitCnt[i] += blocks[i].size();
blkMax[i] = blocks[i].back();
}
if(i+(-i&i) <= b2 and bitCnt[i])
bitCnt[i+(-i&i)] += bitCnt[i];
}
for(int lowb = (-b2 & b2)/2; lowb >= load2X; lowb >>= 1)
bitCnt[b2] += bitCnt[b2-lowb];
}
void _expand(){
vector<vector<_Tp>> blocksOld = move(blocks);
int c = 0;
for(auto &blk : blocksOld) c += blk.size() > 0;
int segn = (c+load2-1)/load2;
blocks.reserve( segn * load2X + 1);
bitCnt.reserve( segn * load2X + 1);
blkMax.reserve( segn * load2X + 1);
int ec = elementCnt;
clear(); elementCnt = ec;
segMax.assign(segn, minVal);
segSize.assign(segn, 0);
for(int i = 0; auto &block : blocksOld){
if(block.size()){
segMax[i>>lg2-1] = block.back();
segSize[i>>lg2-1] += 1;
blkMax.emplace_back(block.back());
bitCnt.emplace_back(block.size());
blocks.emplace_back(move(block));
if( (++i & load2-1) == 0 and i < c){
blocks.resize(blocks.size() + load2);
bitCnt.resize(blocks.size());
blkMax.resize(blocks.size());
}
}
}
for(int i = 1 ; i < bitCnt.size(); ++i)
if(i+(-i&i) < bitCnt.size()) bitCnt[i+(-i&i)] += bitCnt[i];
}
void insert(_Tp x){
++elementCnt;
if(segSize.empty()){
blocks.emplace_back(vector<_Tp>{x});
bitCnt.emplace_back(1);
blkMax.emplace_back(x);
segMax.emplace_back(x);
segSize.emplace_back(1);
return ;
}
auto [bi,it] = _lower_bound(x);
for(int i = bi; i < bitCnt.size(); i += -i & i)
bitCnt[i] += 1;
blocks[bi].insert(it, x);
int segi = (bi - 1) >> lg2;
chmax(blkMax[bi] , x);
chmax(segMax[segi], x);
if(blocks[bi].size() >= load1X){
int bj = (segi<<lg2) | segSize[segi];
int bn = segi+1 << lg2;
if(blocks.size() <= bn){
blocks.insert(blocks.begin()+bi+1, vector<_Tp>(blocks[bi].begin()+load1,blocks[bi].end()));
bitCnt.resize(blocks.size());
blkMax.resize(blocks.size());
}else{
memmove(blocks.data()+bi+2,blocks.data()+bi+1, (bj-bi) * sizeof(vector<_Tp>));
memset(blocks.data()+bi+1 , 0 , sizeof(vector<_Tp>));
blocks[bi+1] = vector<_Tp>(blocks[bi].begin()+load1,blocks[bi].end());
}
blocks[bi].resize(load1);
if(++segSize[segi] == load2X){
_expand();
} else{
_rangeBitModify(segi << lg2 | 1, min<int>(bn, bitCnt.size()-1));
}
}
}
void erase(_Tp x){
if(segMax.empty() or segMax.back() < x) return;
auto [bi,it] = _lower_bound(x);
if(*it > x) return;
--elementCnt;
for(int i = bi; i < bitCnt.size(); i += -i & i)
bitCnt[i] -= 1;
blocks[bi].erase(it);
int segi = (bi - 1) >> lg2;
int bj = (segi<<lg2) | segSize[segi];
if(blocks[bi].empty()){
int bn = segi+1 << lg2;
if(blocks.size() <= bn){
blocks.erase(blocks.begin() + bi);
blkMax.erase(blkMax.begin() + bi);
bitCnt.resize(blocks.size());
if(--segSize[segi] == 0){
segMax.pop_back(), segSize.pop_back();
}else {
_rangeBitModify(segi << lg2 | 1, bitCnt.size() - 1);
if(bi == bj) segMax[segi] = blocks[bj-1].back();
}
}else{
if(--segSize[segi] == 0){
_expand();
}else{
memmove(blocks.data()+bi,blocks.data()+bi+1, (bj-bi) * sizeof(vector<_Tp>));
memset(blocks.data()+bj , 0 , sizeof(vector<_Tp>));
_rangeBitModify(segi << lg2 | 1, bn);
if(bi == bj) segMax[segi] = blocks[bj-1].back();
}
}
}else{
blkMax[bi] = blocks[bi].back();
if(bi == bj) segMax[segi] = blocks[bi].back();
}
}
int size()const{ return elementCnt;}
_Tp operator[](int k){
assert(k >= 0 and k < elementCnt);
int bi = 0;
for(int i = 1 << __lg(bitCnt.size() - 1); i ; i >>= 1 )
if((bi|i) < bitCnt.size() and k - bitCnt[bi|i] >= 0) k -= bitCnt[bi|=i];
return blocks[bi+1][k];
}
int rank(_Tp x){
if(segSize.empty()) return 0;
auto [bi,it] = _lower_bound(x);
int rk = it - blocks[bi].begin();
for(int i = bi - 1; i ; i^=-i&i) rk += bitCnt[i];
return rk;
}
pair<int, Iterator> _prev(pair<int, Iterator> iter){
auto &[bi, it] = iter;
assert(bi > 1 or bi == 1 and it > blocks[bi].begin());
if( it > blocks[bi].begin() ) return {bi , prev(it)};
if( (bi & load2X-1) != 1) return {bi-1,prev(blocks[bi-1].end())} ;
int Segi = ((bi - 1) >> lg2);
bi = (Segi-1 << lg2) | segSize[Segi-1];
return {bi, prev(blocks[bi].end()) };
}
};
using Z = atcoder::modint1000000007;
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n, q;
cin >> n >> q;
vi a(n);
rep(i, 0, n) cin >> a[i];
vector<sortedlistPlus<int>> pos(20);
rep(i, 0, n) rep(j, 0, 20) if (a[i] >> j & 1) pos[j].insert(i);
while (q--) {
int op;
cin >> op;
if (op == 1) {
int i, x;
cin >> i >> x;
i--;
rep(j, 0, 20) if (a[i] >> j & 1) pos[j].erase(i);
a[i] ^= x;
rep(j, 0, 20) if (a[i] >> j & 1) pos[j].insert(i);
} else {
int l, r;
cin >> l >> r;
l--;
Z ans = 0;
rep(j, 0, 20) if (pos[j].rank(r) - pos[j].rank(l)) ans += Z(2).pow(j - 1 + r - l);
cout << ans.val() << "\n";
}
}
}
__baozii__ LV 10
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