Problem: The Little Elephant is playing with the Cartesian coordinates' system. Most of all he likes playing with integer points. The Little Elephant defines an integer point as a pair of integers (x; y), such that 0 ≤ x ≤ w and 0 ≤ y ≤ h. Thus, the Little Elephant knows only (w + 1)·(h + 1) distinct integer points.

The Little Elephant wants to paint a triangle with vertexes at integer points, the triangle's area must be a positive integer. For that, he needs to find the number of groups of three points that form such triangle. At that, the order of points in a group matters, that is, the group of three points (0;0), (0;2), (2;2) isn't equal to the group (0;2), (0;0), (2;2).

Help the Little Elephant to find the number of groups of three integer points that form a nondegenerate triangle with integer area.

Input

A single line contains two integers w and h (1 ≤ w, h ≤ 4000).

Output

In a single output line print an integer — the remainder of dividing the answer to the problem by 1000000007 (109 + 7).

Examples

Input

2 1


Output

36


Input

2 2


Output

240

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int g[4020][4020];
long long n, m, a, b, c, d, s, z, p = 1000000007;
int main() {
  cin >> n >> m, n++, m++;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++)
      if (i && j)
        g[i][j] = i > j ? g[i - j][j] : g[i][j - i];
      else
        g[i][j] = i + j;
  s = n * m % p;
  z = s * (s - 1) % p * (s - 2) % p;
  a = (n >> 1) * (m >> 1);
  b = (n + 1 >> 1) * (m >> 1);
  c = (n >> 1) * (m + 1 >> 1);
  d = (n + 1 >> 1) * (m + 1 >> 1);
  z -= 6 * a * b % p * c % p;
  z -= 6 * b * c % p * d % p;
  z -= 6 * c * d % p * a % p;
  z -= 6 * d * a % p * b % p;
  z -= ((n - 1) * (n - 2) + (m - 1) * (m - 2)) % p * s % p;
  z %= p;
  for (int i = 1; i < n; i++)
    for (int j = 1; j < m; j++)
      if (i || j) z = (z - (g[i][j] - 1) * (n - i) * (m - j) * 12) % p;
  cout << (z + p) % p;
  return 0;
}