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 N = 4000 + 1;
int n, m;
int group[2][2], visit[2][2];
int xcount[N], ycount[N];
int memory[N][N];
int gcd(int i, int j) {
  if (j == 0) {
    return i;
  }
  if (memory[i][j] == -1) {
    memory[i][j] = gcd(j, i % j);
  }
  return memory[i][j];
}
int main() {
  scanf("%d%d", &n, &m);
  memset(group, 0, sizeof(group));
  for (int i = 0; i <= n; ++i) {
    for (int j = 0; j <= m; ++j) {
      group[i & 1][j & 1]++;
    }
  }
  memset(visit, 0, sizeof(visit));
  int result = 0;
  for (int x_0 = 0; x_0 < 2; ++x_0) {
    for (int y_0 = 0; y_0 < 2; ++y_0) {
      int counter_0 = group[x_0][y_0];
      visit[x_0][y_0]++;
      for (int x_1 = 0; x_1 < 2; ++x_1) {
        for (int y_1 = 0; y_1 < 2; ++y_1) {
          int counter_1 =
              (long long)counter_0 * (group[x_1][y_1] - visit[x_1][y_1]) % MOD;
          visit[x_1][y_1]++;
          for (int x_2 = 0; x_2 < 2; ++x_2) {
            for (int y_2 = 0; y_2 < 2; ++y_2) {
              int counter_2 = (long long)counter_1 *
                              (group[x_2][y_2] - visit[x_2][y_2]) % MOD;
              if (((x_1 - x_0) * (y_2 - y_0) - (y_1 - y_0) * (x_2 - x_0)) % 2 ==
                  0) {
                result = (result + counter_2) % MOD;
              }
            }
          }
          visit[x_1][y_1]--;
        }
      }
      visit[x_0][y_0]--;
    }
  }
  memset(xcount, 0, sizeof(xcount));
  memset(ycount, 0, sizeof(ycount));
  for (int i = 0; i <= n; ++i) {
    for (int j = 0; j <= n; ++j) {
      xcount[abs(i - j)]++;
    }
  }
  for (int i = 0; i <= m; ++i) {
    for (int j = 0; j <= m; ++j) {
      ycount[abs(i - j)]++;
    }
  }
  memset(memory, -1, sizeof(memory));
  int counter = 0;
  for (int i = 0; i <= n; ++i) {
    for (int j = 0; j <= m; ++j) {
      if (i != 0 || j != 0) {
        counter = (counter + ((long long)gcd(i, j) - 1) * xcount[i] % MOD *
                                 ycount[j] % MOD) %
                  MOD;
      }
    }
  }
  counter = (3LL * counter) % MOD;
  result = (result + MOD - counter) % MOD;
  printf("%d\n", result);
  return 0;
}