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
#include<cstdio>
using namespace std;
const int mapSize=1e6+5,mod=1e9+7;
int fac[mapSize*2],inv[mapSize*2];
void Init(){
    fac[1]=inv[1]=1;
    for(int i=2;i<=(int)2e6+1;++i) {
        fac[i]=1ll*fac[i-1]*i%mod;
        int res=mod%i,div=mod/i;
        inv[i]=1ll*inv[res]*(mod-div)%mod;
    }
    for(int i=2;i<=(int)2e6+1;++i)
        inv[i]=1ll*inv[i]*inv[i-1]%mod;
    fac[0]=inv[0]=1;
}
int C(int down, int up) {
    return 1ll*fac[down]*inv[up]%mod*inv[down-up]%mod;
}
int rowSum(int rowId, int colL, int colR) {
    int tmp1,tmp2,ret=((tmp1=(C(rowId+1+colR,colR)) - (tmp2=C(rowId+colL,colL-1)))%mod+mod)%mod;
    return ret;
}
int main() {
    Init();
    int r1,c1,r2,c2;
    scanf("%d%d%d%d",&r1,&c1,&r2,&c2);
    int ans = 0;
    for (int rowId = r1; rowId <= r2; ++rowId)
        ans = (ans + rowSum(rowId, c1, c2)) % mod;
    printf("%d\n", ans);
    return 0;
}