Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].

By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.

The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?

Input

The single line of the input contains two integers a, b (1 ≤ a, b ≤ 107).

Output

Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).

Examples

Input

1 1


Output

0


Input

2 2


Output

8

Note

For the first sample, there are no nice integers because <image> is always zero.

For the second sample, the set of nice integers is {3, 5}.
#include <bits/stdc++.h>
double eps = 1e-9;
using namespace std;
long long mod = 1000000007;
int main() {
  std::ios::sync_with_stdio(false);
  long long a, b;
  cin >> a >> b;
  long long total = 0;
  total += ((b * (b - 1)) / 2);
  total = total % mod;
  total = total * a;
  total = total % mod;
  long long x = (a * (a + 1)) / 2;
  x = x % mod;
  long long y = (b * (b - 1)) / 2;
  y = y % mod;
  y = y * b;
  y = y % mod;
  total = total + (x * y) % mod;
  cout << total % mod;
  return 0;
}
