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
def comb(n, r, p):
    x, y = 1, 1
    for i in range(n, n - r, -1):
        x *= i
        y *= i + r - n
        x %= p
        y %= p
    return pow(y, p - 2, p) * x % p

r1, c1, r2, c2 = map(int, input().split())
mod = pow(10, 9) + 7
s1, s2 = c1 + r1, c1 + r2 + 1
t1, t2 = min(c1 + 1, r1 - 1), min(c1 + 1, r2)
comb1 = comb(s1, t1, mod)
comb2 = comb(s2, t2, mod)
u1, u2 = s1 - r1 + 1, s2 - r2
ans = comb2 - comb1
for i in range(1, c2 - c1 + 1):
    comb1 = comb1 * (s1 + i) * pow(u1 + i, mod - 2, mod)
    comb1 %= mod
    comb2 = comb2 * (s2 + i) * pow(u2 + i, mod - 2, mod)
    comb2 %= mod
    ans += comb2
    ans -= comb1
    ans %= mod
print(ans)