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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main{
	static long mod=1000000007 ;
	static InputStream inputstream = System.in;  
	static PrintStream outputstream = System.out;  
	static InputReader in = new InputReader(inputstream);  
	static PrintWriter out = new PrintWriter(outputstream);
	public static void main(String[] args) {
		long a=in.nextLong();
		long b=in.nextLong();
		long sum = (((a*(a+1)/2%mod)*b%mod+a)%mod*(b*(b-1)/2%mod))%mod ;

		System.out.println(sum);
	}

}
class InputReader {  //放到你的主程序的下方咯
    BufferedReader reader;  
    StringTokenizer tokenizer;  
  
    InputReader(InputStream stream) {  
        reader = new BufferedReader(new InputStreamReader(stream));  
        tokenizer = null;  
    }  
  
    public double nextDouble() {
		// TODO Auto-generated method stub
		return Double.parseDouble(next());
	}

	String next() {  
        if (!hasNext())  
        	 throw new RuntimeException();  
        return tokenizer.nextToken();  
    }  
  
    boolean hasNext() {  
        while (tokenizer == null || !tokenizer.hasMoreTokens())  
            try {  
                tokenizer = new StringTokenizer(reader.readLine());  
            } catch (Exception e) {  
                return false;  
            }  
        return true;  
    }  
  
    long nextLong() {  
        return Long.parseLong(next());  
    }  
  
    int nextInt() {  
        return Integer.parseInt(next());  
    }  
}
	  			 	 		   							    		   	