Manao is solving a problem with the following statement:

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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 = 1000 * 150 + 10;
long long a[MAXN], b[MAXN], mn[4 * MAXN], d[4 * MAXN];
void shift(int cur) {
  d[cur * 2] += d[cur];
  mn[cur * 2] += d[cur];
  d[cur * 2 + 1] += d[cur];
  mn[cur * 2 + 1] += d[cur];
  d[cur] = 0;
}
void merge(int cur) { mn[cur] = min(mn[cur * 2], mn[cur * 2 + 1]); }
void add(int lo, int hi, long long val, int cur, int s, int e) {
  if (lo >= hi) return;
  if (lo == s && hi == e) {
    d[cur] += val;
    mn[cur] += val;
    return;
  }
  int mid = (s + e) / 2;
  shift(cur);
  if (lo < mid) add(lo, min(mid, hi), val, cur * 2, s, mid);
  if (hi > mid) add(max(mid, lo), hi, val, cur * 2 + 1, mid, e);
  merge(cur);
}
int main() {
  long long n, m, h;
  cin >> n >> m >> h;
  for (int i = 0; i < m; i++) cin >> b[i], b[i] = h - b[i];
  sort(b, b + m);
  for (int i = 0; i < n; i++)
    cin >> a[i], a[i] = upper_bound(b, b + m, a[i]) - b;
  for (int i = 0; i < m; i++) add(0, i + 1, -1, 1, 0, m);
  int ans = 0;
  for (int i = 0; i < n; i++) {
    add(0, a[i], 1, 1, 0, m);
    if (i >= m) add(0, a[i - m], -1, 1, 0, m);
    if (i >= m - 1) ans += (mn[1] >= 0);
  }
  cout << ans << endl;
  return 0;
}
