Manao is solving a problem with the following statement: He came up with a solution that produces the correct answers but is too slow. You are given the pseudocode of his solution, where the function getAnswer calculates the answer to the problem: getAnswer(a[1..n], b[1..len], h) answer = 0 for i = 1 to n-len+1 answer = answer + f(a[i..i+len-1], b, h, 1) return answerf(s[1..len], b[1..len], h, index) if index = len+1 then return 1 for i = 1 to len if s[index] + b[i] = h mem = b[i] b[i] = 0 res = f(s, b, h, index + 1) b[i] = mem if res 0 return 1 return 0 Your task is to help Manao optimize his algorithm.

输入描述:

The first line contains space-separated integers n, len and h (1 ≤ len ≤ n ≤ 150000; 1 ≤ h ≤ 109). The second line contains len space-separated integers b1, b2, ..., blen (1 ≤ bi ≤ 109). The third line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).

输出描述:

Print a single number — the answer to Manao's problem.