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>

typedef long long ll;
using namespace std;
const ll mod = 1000000007;
const ll mod998 = 998244353;
const ll intmax = 2147483647;
const ll llmax = 9223372036854775807;
const char sp = ' ';



int r1, c1, r2, c2;
ll f[3000001], res;

inline ll pw(ll x, int y) {
	ll a = 1;
	while (y) {
		if (y & 1)a = a*x%mod;
		x = x*x%mod;
		y /= 2;
	}
	return a;
}

inline ll modinv(ll x) {
	return pw(x, mod - 2);
}

inline ll comb(int n, int r) {
	return f[n] * modinv(f[n - r] * f[r] % mod) % mod;
}

int main() {
	cin >> r1 >> c1 >> r2 >> c2;
	f[0] = 1;
	for (ll i = 1; i <= 3000000; i++) {
		f[i] = f[i - 1] * i%mod;
	}
	for (int i = r1; i <= r2; i++) {
		res += comb(i + 1 + c2, i + 1);
		res += mod - comb(i + c1, i + 1);
		res %= mod;
	}
	cout << res << endl;
}