#include <bits/stdc++.h>
using namespace std;
long long W, H, mod = 1000000007;
void add(long long &x, long long y) { x = (x + y) % mod; }
void sbs(long long &x, long long y) {
  x = (x - y) % mod;
  if (x < 0) x += mod;
}
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
void solve() {
  long long wn[2], hn[2];
  wn[0] = W / 2;
  wn[1] = W - wn[0];
  hn[0] = H / 2;
  hn[1] = H - hn[0];
  long long ans = 0;
  for (int x1 = 0; x1 <= 1; x1++)
    for (int x2 = 0; x2 <= 1; x2++)
      for (int x3 = 0; x3 <= 1; x3++)
        for (int y1 = 0; y1 <= 1; y1++)
          for (int y2 = 0; y2 <= 1; y2++)
            for (int y3 = 0; y3 <= 1; y3++)
              if (((x1 - x3) * (y2 - y3) - (x2 - x3) * (y1 - y3)) % 2 == 0) {
                add(ans, (((wn[x1] * wn[x2] * wn[x3]) % mod) * hn[y1] * hn[y2] *
                          hn[y3]) %
                             mod);
              }
  sbs(ans, W * H);
  sbs(ans, H * ((W * W * W - W) % mod) + W * ((H * H * H - H) % mod));
  for (int dx = 1; dx < W; dx++) {
    for (int dy = 1; dy < H; dy++) {
      sbs(ans, 2 * 6 * (W - dx) * (H - dy) * (gcd(dx, dy) - 1));
      sbs(ans, 2 * 3 * (W - dx) * (H - dy) * 2);
    }
  }
  cout << ans << endl;
}
int main() {
  while (cin >> W >> H) {
    W++;
    H++;
    solve();
  }
}

### Prompt

Please formulate a CPP solution to the following 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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long W, H, mod = 1000000007;
void add(long long &x, long long y) { x = (x + y) % mod; }
void sbs(long long &x, long long y) {
  x = (x - y) % mod;
  if (x < 0) x += mod;
}
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
void solve() {
  long long wn[2], hn[2];
  wn[0] = W / 2;
  wn[1] = W - wn[0];
  hn[0] = H / 2;
  hn[1] = H - hn[0];
  long long ans = 0;
  for (int x1 = 0; x1 <= 1; x1++)
    for (int x2 = 0; x2 <= 1; x2++)
      for (int x3 = 0; x3 <= 1; x3++)
        for (int y1 = 0; y1 <= 1; y1++)
          for (int y2 = 0; y2 <= 1; y2++)
            for (int y3 = 0; y3 <= 1; y3++)
              if (((x1 - x3) * (y2 - y3) - (x2 - x3) * (y1 - y3)) % 2 == 0) {
                add(ans, (((wn[x1] * wn[x2] * wn[x3]) % mod) * hn[y1] * hn[y2] *
                          hn[y3]) %
                             mod);
              }
  sbs(ans, W * H);
  sbs(ans, H * ((W * W * W - W) % mod) + W * ((H * H * H - H) % mod));
  for (int dx = 1; dx < W; dx++) {
    for (int dy = 1; dy < H; dy++) {
      sbs(ans, 2 * 6 * (W - dx) * (H - dy) * (gcd(dx, dy) - 1));
      sbs(ans, 2 * 3 * (W - dx) * (H - dy) * 2);
    }
  }
  cout << ans << endl;
}
int main() {
  while (cin >> W >> H) {
    W++;
    H++;
    solve();
  }
}

```