Manao is solving a problem with the following statement:

<image>

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 ≤ 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
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 150000 + 10;
int len, n, h;
int a[MAXN], b[MAXN];
int dp[1 << 20], all[1 << 20];
inline void go(int root, int lo, int hi, int s, int e, int key) {
  if (hi < s || e < lo) return;
  if (s <= lo && hi <= e) {
    all[root] += key;
    dp[root] += key;
    return;
  }
  int mid = (lo + hi) / 2;
  go(root * 2, lo, mid, s, e, key);
  go(root * 2 + 1, mid + 1, hi, s, e, key);
  dp[root] = min(dp[root * 2], dp[root * 2 + 1]) + all[root];
}
inline void build(int root, int lo, int hi) {
  if (lo == hi) {
    dp[root] = -lo;
    return;
  }
  int mid = (lo + hi) / 2;
  build(root * 2, lo, mid);
  build(root * 2 + 1, mid + 1, hi);
  dp[root] = -hi;
}
int main() {
  cin >> n >> len >> h;
  for (int i = 0; i < len; i++) cin >> b[i];
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(b, b + len);
  int ret = 0;
  build(1, 0, len - 1);
  for (int i = 0; i < n; i++) {
    int poi = lower_bound(b, b + len, h - a[i]) - b;
    go(1, 0, len - 1, poi, len - 1, 1);
    if (len <= i + 1) {
      ret += (dp[1] > 0);
      poi = lower_bound(b, b + len, h - a[i - len + 1]) - b;
      go(1, 0, len - 1, poi, len - 1, -1);
    }
  }
  cout << ret << endl;
  return 0;
}
