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 java.io.PrintWriter;
public class Main{
	static long mod=1000000007;
	static long[] fact;
	static long[] inv;
	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 ans=0;
		fact=new long[c2+r2+2];
		fact[1]=1;
		for(int i=2; i<=c2+r2+1; i++){
			fact[i]=(fact[i-1]*i)%mod;
		}
		inv=new long[c2+r2+2];
		inv[c2+r2+1]=pow(fact[c2+r2+1],mod-2);
		for(int i=c2+r2; i>=0; i--){
			inv[i]=(inv[i+1]*(i+1))%mod;
		}
		for(int i=c1; i<=c2; i++){
			ans+=comb(i+r2+1,i+1)-comb(i+r1,i+1)+mod;
			ans%=mod;
		}
		System.out.println(ans);
	}
	static long comb(int t,int y){
		long re=1;
		re*=fact[t];
		re*=inv[y];
		re%=mod;
		re*=inv[t-y];
		return re%mod;
	}
	
	static long pow(long p,long q){
		long res=1;
		while(q>0){
			if((q & 1)==1){
				res*=p;
				res%=mod;
			}
			q>>=1;
			p*=p;
			p%=mod;
		}
		return res;
	}
}
