Problem3354--Optimize!

3354: Optimize!

[Creator : ]
Time Limit : 2.000 sec  Memory Limit : 256 MiB

Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 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≤lenn≤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).

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

Source/Category