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.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int r1 = sc.nextInt();
		int c1 = sc.nextInt();
		int r2 = sc.nextInt();
		int c2 = sc.nextInt();
		
		// 計算
		long result = 0;
		int MOD = 1000000007;
		Combination comb = new Combination(r2+c2+2);
		result += comb.combination(r2+c2+2, c2+1)-1;
		result %= MOD;
		result -= comb.combination(r2+c1+1, c1)-1;
		result %= MOD;
		result -= comb.combination(r1+c2+1, r1)-1;
		result %= MOD;
		result += comb.combination(r1+c1, c1)-1;
		result %= MOD;
		if(result < 0) result += MOD;
		
		// 出力
		System.out.println(result);
	}
}

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