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 {

// global
static long fact[];
static long inverse[];
static int mod = 1_000_000_007;

static long pow(long a,int n) {
    long res=1;
    while (n>0) {
        if ((n-n/2*2)==1) {
            res=res*a%mod;
        }
        a=a*a%mod;
        n>>=1;
    }
    return res;
}

static long modinv(long n) {
    return pow(n, mod-2);
}

static long comb(int n,int k){
    if(n<0 || k<0 || n<k)return 0;
    return fact[n]*(inverse[k]*inverse[n-k]%mod) %mod;
}


    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        // main method
        fact=new long[2400005];
        fact[0]=1;
        inverse=new long[2400005];
        inverse[0]=1;
        for(int i=1;i<2400005;i++){
            fact[i]=(fact[i-1]*(long)i)%mod;
            inverse[i]=modinv(fact[i]);
        }

        int r1 = sc.nextInt();
        int c1 = sc.nextInt();
        int r2 = sc.nextInt();
        int c2 = sc.nextInt();
        long ans = 0L;
        for (int i=r1;i<r2+1;i++) {
            ans = (ans+comb(i+c2+1, c2)-comb(i+c1, c1-1))%mod;
        }
        ans = (ans+mod)%mod;
        System.out.println(ans);
    }
}
