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;
long long w, h, n, ans, a, b, c, d, p = 1000000007;
long long gcd[4010][4010];
int main() {
  int i, j;
  cin >> w >> h;
  w++;
  h++;
  for (i = 0; i <= w; ++i)
    for (j = 0; j <= h; ++j)
      if (i && j)
        gcd[i][j] = i > j ? gcd[i - j][j] : gcd[i][j - i];
      else
        gcd[i][j] = i + j;
  n = w * h % p;
  ans = n * (n - 1) % p * (n - 2) % p;
  a = (w >> 1) * (h >> 1);
  b = (w + 1 >> 1) * (h >> 1);
  c = (w >> 1) * (h + 1 >> 1);
  d = (w + 1 >> 1) * (h + 1 >> 1);
  ans -= a * b % p * c % p * 6 % p;
  ans -= a * b % p * d % p * 6 % p;
  ans -= a * d % p * c % p * 6 % p;
  ans -= d * b % p * c % p * 6 % p;
  ans %= p;
  for (i = 0; i <= w; ++i)
    for (j = 0; j <= h; ++j)
      if (i || j)
        ans = (ans - (gcd[i][j] - 1) * (w - i) * (h - j) * 6 * ((i && j) + 1)) %
              p;
  cout << (ans + p) % p << endl;
}