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 int MOD = 1e9 + 7;
const int N = 1e6 + 5;
ll fact[2 * N];

ll binpow(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 % m;
}

ll inverse(ll x) {
	return binpow(x, MOD - 2, MOD);
}

ll cc(ll n, ll k) {
	return fact[n] * inverse(fact[k]) % MOD * inverse(fact[n - k]) % MOD;
}

int main()
{
	ll r1, c1, r2, c2;
	scanf("%lld%lld%lld%lld", &r1, &c1, &r2, &c2);
	fact[0] = 1;
	for (int i = 1; i <= r2 + c2 + 2; i++) {
		fact[i] = fact[i - 1] * i % MOD;
	}
	ll ans = (cc(r1+c1, c1) + cc(r2+c2+2, c2+1) - cc(r1+c2+1, c2+1) - cc(r2+c1+1, c1)) % MOD;
	printf("%lld\n", (ans + MOD) % MOD);
	return 0;
}