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E. Optimize!

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputManao 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 answer

f(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.

Input

The first line contains space-separated integers *n*, *len* and *h* (1 ≤ *len* ≤ *n* ≤ 150000; 1 ≤ *h* ≤ 10^{9}). The second line contains *len* space-separated integers *b*_{1}, *b*_{2}, ..., *b*_{len} (1 ≤ *b*_{i} ≤ 10^{9}). The third line contains *n* space-separated integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{9}).

Output

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

Examples

Input

5 2 10

5 3

1 8 5 5 7

Output

2

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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