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;

const int MOD = 1e9+7;
const int MAX = 2e6+10;

typedef long long ll;

ll f[MAX];
ll invf[MAX];

ll bigmod(ll a, ll b, ll m){
	a%=m;
	ll res = 1;
	while(b > 0){
		if(b&1)	res=(res*a)%m;
		a = (a*a)%m;
		b >>= 1;
	}
	return res;
}

void precompute(){
	f[0] = 1;
	for (int i = 1; i < MAX; ++i){
		f[i] = f[i-1]*i%MOD;
	}
	invf[MAX-1] = bigmod(f[MAX-1], MOD-2, MOD);
	for (int i = MAX-2; i > 0; --i){
		invf[i] = invf[i+1]*(i+1)%MOD;
	}
	invf[0] = 1;
}

ll nCr(ll n, ll r){
	return f[n]*invf[n-r]%MOD*invf[r]%MOD;
}

int main(){
	precompute();
	ll r1, c1;	cin >> r1 >> c1;
	ll r2, c2;	cin >> r2 >> c2;
	ll ans = 0;
	for (ll i = r1; i <= r2; ++i){
		ans += nCr(i+c2+1, i+1) - nCr(i+c1, i+1) % MOD;
		ans %= MOD;
	}
	cout << (ans+MOD)%MOD << endl;
	return 0;
}
