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}.
#!/usr/bin/env python
#coding: utf-8
#a = [([0] * 3) for _ in xrange(4)]
#a = [1, 5, 2, 6, 9, 4]
#b = sorted(a, cmp = lambda x, y: cmp(y, x), reverse = True)
#class Node:
#	def __init__(self, X, Y):
#		self.x = X
#		self.y = Y
#a = []
#a.append(Node(1, 2))
#print a[0].x, a[0].y

#while true:
#    try:
#        s = raw_input()
#    except:                # 当遇到文件终结的时候会扔出 EOFError
#        print "EOF"
#        break

in1 = lambda : int(raw_input())
in2 = lambda : map(int, raw_input().split())

def gcd(a, b) :
    if (b == 0):
        return a
    return gcd(b, a % b)

n4 = 250000002
MOD = 1000000007

a, b = map(int, raw_input().split())

#ans = (1 / 4) * a * b * (b - 1) * (b + a * b + 2)
print n4 * a % MOD * b % MOD * (b - 1) % MOD * (b + a * b % MOD + 2) % MOD
