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Time Limit: 0.5 s

Memory Limit: 256.0 MB

Description

In the bustling land of Algorithma, a new competitive event is underway to test the sharp minds of coders and mathematicians. The challenge? To explore vast grids and uncover the total number of perfect square sub-grids hidden within them. These square sub-grids are highly prized by the kingdom, as they’re known to contain hidden patterns and secrets that only the sharpest minds can reveal.

Given a large grid with dimensions \(H × W\), your task is to count the number of perfect square sub-grids that can be formed within it. A sub-grid is defined by selecting any top-left and bottom-right corners within the grid, and a perfect square sub-grid has equal height and width.

For example, in a \(4×3\) grid:

• \(A\) \(1×1\) sub-grid is a perfect square.
• \(A\) \(2×2\) sub-grid is also a perfect square.
• However, \(A\) \(3×2\) sub-grid is not a perfect square.

Input

The input contains two integers:

• \(H\) \(( 1≤H≤10^5 )\): the height of the grid.
• \(W\) \((1≤W≤10^5 )\): the width of the grid.

Output

Print a single integer, the total number of perfect square sub-grids that can be found in the \(H×W\) grid.

Sample

5 3

26

Explanation

The \(5×3\) grid has the following perfect square sub-grids:

• \(1×1\): \(15\) sub-grids
• \(2×2\): \(8\) sub-grids
• \(3×3\): \(3\) sub-grids
  The total number of perfect square sub-grids is 15 + 8 + 3 = \(26\).