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>
#define l_ength size
const int inf = (1<<30);
using ll = long long;
using namespace std;
const ll mod = 1000000007;

const int bound = 2000020;
ll fact[bound], fact_inv[bound];

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

void init(){
	fact[0] = 1;
	int b = bound-10;
	for( int i = 0; i < b; ++i ){
		fact[i+1] = fact[i]*(i+1) % mod;
	}
	fact_inv[b] = power(fact[b], mod-2);
	for( int i = b-1; i >= 0; --i ){
		fact_inv[i] = fact_inv[i+1]*(i+1) % mod;
	}
}

ll comb( ll n, ll r ){
	if( n < r ) return 0;
	return ( fact[n]*fact_inv[r] ) % mod * fact_inv[n-r] % mod;
}

ll seq( ll x, ll y ){
	return ( comb(x+y+2, x+1)+mod-1 ) % mod;
}

int main(){
	init();
	ll a, b, c, d; cin >> a >> b >> c >> d;
	cout << ( seq(c, d) - seq(a-1, d) - seq(c, b-1) + seq(a-1, b-1) + 10*mod ) % mod << endl;
}