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;
#define all(V) V.begin(),V.end()
using ll = long long;
const ll MOD = 1000000007;

ll factr[2000010];

ll modpow(ll x, ll y) {
	x %= MOD;
	ll ans = 1;
	while (y) {
		if (y & 1)ans *= x;
		y /= 2;
		x *= x;
		ans %= MOD;
		x %= MOD;
	}
	return ans;
}

ll moddiv(ll a, ll b) {
	return a * modpow(b, MOD - 2) % MOD;
}

ll solve(ll X, ll Y) {
	ll ans = 0;
	
	for (ll i = 0;i <= X;i++) {
		ans += moddiv(moddiv(factr[i + Y + 1], factr[i + 1]), factr[Y]);
		ans %= MOD;
	}
	return ans;
}

int main() {
	ll r1, r2, c1, c2;
	cin >> r1 >> c1 >> r2 >> c2;

	factr[0] = 1;
	for (ll i = 1;i < 2000010;i++)factr[i] = factr[i - 1] * i % MOD;

	ll ans = solve(r2, c2) - solve(r2, c1 - 1) - solve(r1 - 1, c2) + solve(r1 - 1, c1 - 1);
	ans %= MOD;
	if (ans < 0)ans += MOD;

	cout << ans << endl;
}