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())
L = 10 ** 9 + 7

# 互除法
def get_euclidian (A, B):
  if B == 1:
    return (1)
  else:
    return (int((1 - A * get_euclidian (B, A % B)) / B))

# 階乗計算
F = [1]
for i in range(1, r2 + c2 + 3):
  F.append((F[i - 1] * i) % L)

# 組み合わせ計算
def get_combi (n, r):

  Euc = get_euclidian(L, (F[r] * F[n - r]) % L)
  return ((F[n] * Euc) % L)

combi1 = get_combi(r2 + c2 + 2, r2 + 1)
combi2 = get_combi(r2 + c1 + 1, c1)
combi3 = get_combi(r1 + c2 + 1, r1)
combi4 = get_combi(r1 + c1, r1)

print ((int(combi1 - combi2 - combi3 + combi4) + L) % L)