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 = 1000000007

def pow(x, n):
    ret = 1
    while n > 0:
        if (n & 1) == 1:
            ret = (ret * x) % mod
        x = (x * x) % mod
        n //= 2
    return ret

def fac(n):
    ret = 1
    for i in range(1, n + 1):
        ret = (ret * i) % mod
    return ret

def facinv(n):
    return pow(fac(n), mod - 2)

def cmb(n, k):
    if k < 0 or k > n:
        return 0
    return ((fac(n) * facinv(k)) % mod * facinv(n - k)) % mod

def rect(r, c):
    return cmb(r + c, c)

ret = (rect(r2 + 1, c2 + 1) - rect(r1, c2 + 1) - rect(r2 + 1, c1) + rect(r1, c1) + mod + mod) % mod
print(ret)
