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.*;
import java.util.*;

public class A {

	static final int MOD = 1000000007;

	static void solve() throws IOException {
		int a = nextInt();
		int b = nextInt();
		int ans = smart(a, b);
		out.println(ans);
	}

	static int stupid(int a, int b) {
		int ans = 0;
		for (int mod = 1; mod < b; mod++) {
			for (long div = mod; div <= (long) mod * a; div += mod) {
				ans = (int) ((ans + div % MOD * b % MOD + mod) % MOD);
			}
		}
		return ans;
	}

	private static int smart(int a, int b) {
		int sumMod = (int) ((long) b * (b - 1) / 2 % MOD);
		int sumA = (int) ((long) a * (a + 1) / 2 % MOD);
		int ans = (int) ((long) sumMod * a % MOD);
		ans = (int) ((ans + (long) sumA * sumMod % MOD * b) % MOD);
		return ans;
	}

	static BufferedReader br;
	static StringTokenizer st;
	static PrintWriter out;

	public static void main(String[] args) throws IOException {
		InputStream input = System.in;
		PrintStream output = System.out;
		File file = new File("a.in");
		if (file.exists() && file.canRead()) {
			input = new FileInputStream(file);
			output = new PrintStream("a.out");
		}
		br = new BufferedReader(new InputStreamReader(input));
		out = new PrintWriter(output);
		solve();
		out.close();
		br.close();
	}

	static boolean hasNext() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String line = br.readLine();
			if (line == null) {
				return false;
			}
			st = new StringTokenizer(line);
		}
		return true;
	}

	static String next() throws IOException {
		return hasNext() ? st.nextToken() : null;
	}

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

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

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