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.Scanner;

public class Main {
	static final long MOD = 1000000007;
	static long modpow(long n, long y){
		if(y == 0){
			return 1;
		}else if(y == 1){
			return n % MOD;
		}else{
			if(y % 2 == 0){
				long r = modpow(n , y / 2);
				return (r * r) % MOD;
			}else{
				long r = modpow(n , y / 2);
				long r2 = (r * r) % MOD;
				return (r2 * n) % MOD;				
			}
		}
	}
	static long modinv(long n){
		return modpow(n , MOD - 2);
	}

	static long g(int R , int C){
		long fact[] = new long[R + C + 3];
		fact[0] = 1;
		fact[1] = 1;
		for(int i = 2 ; i < fact.length ; ++i){
			fact[i] = ((long)(i) * fact[i - 1]) % MOD;
		}
		long pat = fact[R + C + 2] ;
		pat = (pat * modinv(fact[R + 1])) % MOD;
		pat = (pat * modinv(fact[C + 1])) % MOD;
		return pat;
	}
	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();
		long ret = g(r2 , c2) + g(r1 - 1 , c1 - 1) + 2 * MOD - (g(r1 - 1 , c2) + g(r2, c1 - 1));
		System.out.println(ret % MOD);
	}
}
