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;
const int MOD = 1000000007;
const int MAX_N = 4000 + 10;
int n, m;
int gcd[MAX_N][MAX_N];
long long f[2][2];
long long ans;
inline long long binom(long long n) { return n * (n - 1) * (n - 2) % MOD; }
int main(int argc, char *argv[]) {
  for (int i = 1; i < MAX_N; i++) {
    for (int j = 1; j < MAX_N; j++) {
      if (i > j) {
        gcd[i][j] = gcd[i - j][j];
      } else if (i < j) {
        gcd[i][j] = gcd[i][j - i];
      } else {
        gcd[i][j] = i;
      }
    }
  }
  cin >> n >> m;
  n++;
  m++;
  long long nm = n * m;
  for (int a = 1; a < n; a++) {
    for (int b = 1; b < m; b++)
      if (gcd[a][b] > 1) {
        ans += (long long)(gcd[a][b] - 1) * (n - a) * (m - b) * 12;
        ans %= MOD;
      }
  }
  ans += binom(n) * m + binom(m) * n;
  ans = -ans;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      f[i & 1][j & 1]++;
    }
  }
  for (int x1 = 0; x1 < 2; x1++) {
    for (int y1 = 0; y1 < 2; y1++) {
      f[x1][y1]--;
      long long sum1 = 0;
      for (int x2 = 0; x2 < 2; x2++) {
        for (int y2 = 0; y2 < 2; y2++) {
          long long sum2 = 0;
          f[x2][y2]--;
          for (int x3 = 0; x3 < 2; x3++) {
            for (int y3 = 0; y3 < 2; y3++) {
              int area = (x3 - x1) * (y2 - y1) - (y3 - y1) * (x2 - x1);
              if (area % 2 == 0) {
                sum2 += f[x3][y3];
              }
            }
          }
          f[x2][y2]++;
          sum1 += sum2 * f[x2][y2];
          sum1 %= MOD;
        }
      }
      f[x1][y1]++;
      ans += sum1 * f[x1][y1];
      ans %= MOD;
    }
  }
  cout << ans << endl;
  return 0;
}