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;
using ll = long long;
const ll mod = 1e9L + 7;
const ll inv2 = (mod + 1) / 2;
const ll inv3 = (mod + 1) / 3;
const ll inv6 = (mod + 1) / 6;
ll cn2(ll n) { return n * (n - 1) % mod * inv2 % mod; }
ll cn3(ll n) { return n * (n - 1) % mod * (n - 2) * inv6 % mod; }
const int N = 4e3L + 11;
int gcd[N][N];
int main() {
  for (int k = 1; k < N; k++)
    for (int i = 0; i < N; i += k)
      for (int j = 0; j < N; j += k) gcd[i][j] = k;
  ios ::sync_with_stdio(0);
  int n, m;
  cin >> n >> m;
  ll ans = 0;
  for (int i = 0; i < 2; i++)
    for (int j = 0; j < 2; j++) {
      ll c[4];
      for (int s = 0; s < 2; s++)
        for (int t = 0; t < 2; t++) {
          ll a = (((i ^ s) & 1) ? (n + 1) / 2 : n / 2 + 1);
          ll b = (((j ^ t) & 1) ? (m + 1) / 2 : m / 2 + 1);
          c[s * 2 + t] = a * b;
        }
      c[0]--;
      ll tmp = 0;
      for (int s = 0; s < 4; s++)
        for (int t = s; t < 4; t++) {
          int x = (s >> 1) * (t & 1) + (s & 1) * (t >> 1);
          if (x % 2 == 0) {
            if (s == t)
              tmp += cn2(c[s]);
            else
              tmp += c[s] * c[t];
            tmp %= mod;
          }
        }
      ll a = ((i & 1) ? (n + 1) / 2 : n / 2 + 1);
      ll b = ((j & 1) ? (m + 1) / 2 : m / 2 + 1);
      ans += tmp * a * b;
      ans %= mod;
    }
  ans = ans * inv3 % mod;
  for (int i = 0; i <= n; i++)
    for (int j = 0; j <= m; j++)
      if ((i > 0 || j > 0) && gcd[i][j] == 1) {
        for (int k = 0; k * i <= n && k * j <= m; k++) {
          ll t = ll(n - k * i + 1) * (m - k * j + 1);
          if ((k + 1) * i <= n && (k + 1) * j <= m)
            t -= ll(n - (k + 1) * i + 1) * (m - (k + 1) * j + 1);
          ans -= t * cn2(k);
          if (i > 0 && j > 0) ans -= t * cn2(k);
          ans %= mod;
        }
      }
  cout << (ans * 6 % mod + mod) % mod << '\n';
  return 0;
}