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 gcd(int x, int y) { return !y ? x : gcd(y, x % y); }
int main() {
  int W, H, w, h, r, t;
  for (scanf("%d%d", &W, &H), r = 0, w = 1; w <= W; w++)
    for (h = 1; h <= H;
         r = (r + (long long)t * (W - w + 1) * (H - h + 1)) % 1000000007, h++) {
      if (w % 2 && h % 2)
        t = (w / 2 + 1) * (h / 2 + 1) + ((w + 1) / 2) * ((h + 1) / 2);
      else if (w % 2)
        t = (h / 2 + 1) * (w + 1);
      else if (h % 2)
        t = (w / 2 + 1) * (h + 1);
      else
        t = (w + 1) * (h + 1);
      t -= gcd(w, h) + 1;
      t *= 2;
      if (w * h % 2 == 0)
        t += (w + h - 2) * 2 + (w - 1) * (h - 1) * 4 - (h / 2) * (w / 2) * 4;
      else
        t += (w / 2) * (h / 2) * 4;
    }
  printf("%I64d\n", (long long)r * 6 % 1000000007);
  return 0;
}