Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.

Let us define a function f(r, c) as follows:

* f(r,c) :=  (The number of paths from the point (0, 0) to the point (r, c) that Snuke can trace by repeating the operation above)



Given are integers r_1, r_2, c_1, and c_2. Find the sum of f(i, j) over all pair of integers (i, j) such that r_1 ≤ i ≤ r_2 and c_1 ≤ j ≤ c_2, and compute this value modulo (10^9+7).

Constraints

* 1 ≤ r_1 ≤ r_2 ≤ 10^6
* 1 ≤ c_1 ≤ c_2 ≤ 10^6
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


r_1 c_1 r_2 c_2


Output

Print the sum of f(i, j) modulo (10^9+7).

Examples

Input

1 1 2 2


Output

14


Input

314 159 2653 589


Output

602215194
import java.util.*;

public class Main {
    static final int MOD = 1000000007;
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int r1 = sc.nextInt();
		int c1 = sc.nextInt();
		int r2 = sc.nextInt();
		int c2 = sc.nextInt();
		Combination cmb = new Combination(r2 + c2 + 3);
		long ans = cmb.getComb(r2 + c2 + 2, r2 + 1) - cmb.getComb(r2 + c1 + 1, c1) - cmb.getComb(r1 + c2 + 1, r1) + cmb.getComb(r1 + c1, c1) + MOD + MOD; 
		ans %= MOD;
		System.out.println(ans);
   }

}

class Combination {
    static final int MOD = 1000000007;
    long[] fac;
    long[] finv;
    long[] inv;
    
    public Combination (int size) {
        fac = new long [size];
        finv = new long [size];
        inv = new long [size];
        fac[0] = 1;
        fac[1] = 1;
        finv[0] = 1;
        finv[1] = 1;
        inv[1] = 1;
        for (int i = 2; i < size; i++) {
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }
    
    
    public long getComb(int n, int k) {
        if (n < k || n < 0 || k < 0) {
            return 0;
        }
        return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
    }
    
}

