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 long long mod = 1000000007ll;
long long parity_ways[2][2];
int gcd[4001][4001];
void modadd(long long &a, long long b) {
  a += b;
  if (a >= mod) {
    a -= mod;
  }
}
int main() {
  int w, h;
  scanf("%d %d", &w, &h);
  ++w;
  ++h;
  for (int a = 0; a < 2; ++a) {
    for (int b = 0; b < 2; ++b) {
      parity_ways[a][b] =
          (long long)(w / 2 + (!a && (w & 1))) * (h / 2 + (!b && (h & 1)));
    }
  }
  long long sol = 0;
  for (int a = 0; a < 2; ++a) {
    for (int b = 0; b < 2; ++b) {
      for (int c = 0; c < 2; ++c) {
        for (int d = 0; d < 2; ++d) {
          for (int e = 0; e < 2; ++e) {
            for (int f = 0; f < 2; ++f) {
              int x1 = c - a, y1 = d - b, x2 = e - a, y2 = f - b;
              int area = x1 * y2 - y1 * x2;
              if (area < 0) {
                area = -area;
              }
              if (area % 2 == 0) {
                modadd(sol, parity_ways[a][b] * parity_ways[c][d] % mod *
                                parity_ways[e][f] % mod);
              }
            }
          }
        }
      }
    }
  }
  long long all_points = (long long)w * h % mod;
  long long zeros = all_points;
  modadd(zeros, all_points * (all_points - 1) % mod * 3 % mod);
  modadd(zeros, all_points * (w - 1) % mod * (w - 2) % mod);
  modadd(zeros, all_points * (h - 1) % mod * (h - 2) % mod);
  for (int i = 0; i < w; ++i) {
    for (int j = 0; j < h; ++j) {
      if (i == 0)
        gcd[i][j] = j;
      else if (j == 0)
        gcd[i][j] = i;
      else if (i < j)
        gcd[i][j] = gcd[j % i][i];
      else
        gcd[i][j] = gcd[i % j][j];
    }
  }
  for (int x = 1; x < w; ++x) {
    for (int y = 1; y < h; ++y) {
      if (gcd[x][y] >= 2) {
        modadd(zeros,
               (gcd[x][y] - 1) * (w - x) % mod * (h - y) % mod * 12 % mod);
      }
    }
  }
  sol = (sol - zeros + mod) % mod;
  printf("%d\n", int(sol));
  return 0;
}