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
r1,c1,r2,c2 = map(int,input().split())

MOD = 10**9+7
MAXN = r2+c2+5
fac = [1,1] + [0]*MAXN
for i in range(2,MAXN+2):
    fac[i] = fac[i-1] * i % MOD

def inv(n):
    return pow(n,MOD-2,MOD)

def comb(n,r):
    if n < r: return 0
    if n < 0 or r < 0: return 0
    return fac[n] * inv(fac[r]) * inv(fac[n-r]) % MOD

r2,c2 = r2+1,c2+1
ans = comb(r2+c2,r2) - comb(r2+c1,r2) - comb(r1+c2,r1) + comb(r1+c1,r1)
ans %= MOD
print(ans)