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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll N=2e6+5,mod=1e9+7;
ll fct[N],inv[N],invfct[N];
void init(){
    fct[0]=fct[1]=1;
	inv[1]=1;
	invfct[0]=invfct[1]=1;
	for(ll i=2;i<N;i++){
		fct[i]=i*fct[i-1]%mod;
		inv[i]=ll(mod-inv[mod%i])*(mod/i)%mod;
		invfct[i]=ll(inv[i])*invfct[i-1]%mod;
	}
}
inline ll ncr(ll n,ll r){
    if(n<0 || n-r<0)return 0;
    ll val = fct[n]*invfct[r];
    val%=mod;
    val = val*invfct[n-r];
    val%=mod;
    return val;
}
int main(){
    ios_base:: sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL);
    init();
    ll r1,c1,r2,c2;cin>>r1>>c1>>r2>>c2;
    ll ans = 0;
    for(ll r=r1;r<=r2;r++){
        ll val = ncr(r+c2+1,r+1) - ncr(r+c1,r+1);
        val = val + mod;
        val%=mod;
        ans = ans + val;
        ans%=mod;
       // cout<<r<<" "<<val<<endl;
    }
    cout<<ans;
}


