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}.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.StringTokenizer;

import javax.swing.ButtonGroup;

public class zizo {
	
	public static void main(String args[]) throws IOException {
		Scanner zizo=new Scanner (System.in);
		PrintWriter wr=new PrintWriter(System.out);
		
		long a=zizo.nextInt();
		long b=zizo.nextInt();
		long ans=0;
		for(int k=1;k<=a;k++)
            ans = (ans + (((k * b + 1)%1_000_000_007) * (b * (b-1) / 2 %1_000_000_007))%1_000_000_007)%1_000_000_007;
		wr.println(ans);
		wr.close();
	}
}

class Scanner {
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream s) {
		br = new BufferedReader(new InputStreamReader(s));
	}

	public String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine(), " ");
		return st.nextToken();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	public long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	public String nextLine() throws IOException {
		return br.readLine();
	}

	public boolean ready() throws IOException {
		return br.ready();
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

}