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 = 2e5 + 10;
int n, m, h, seg[MAXN * 4], k[MAXN], b[MAXN], a[MAXN], flag[MAXN * 4];
int calc(int x) {
  int s = -1, e = m;
  while (e - s > 1) {
    int mid = (s + e) / 2;
    if (b[mid] + x >= h)
      s = mid;
    else
      e = mid;
  }
  return s;
}
void update(int s, int e, int ind) {
  int mid = (s + e) / 2;
  int ans1 = seg[((ind)*2)] - (e - mid), ans2 = seg[(((ind)*2) + 1)];
  seg[ind] = min(ans1, ans2);
}
void relax(int s, int e, int ind) {
  int val = flag[ind];
  flag[((ind)*2)] += val;
  flag[(((ind)*2) + 1)] += val;
  seg[((ind)*2)] += val;
  seg[(((ind)*2) + 1)] += val;
  flag[ind] = 0;
}
void add(int s, int e, int ind, int x, int y, int val) {
  if (s >= y or e <= x) return;
  if (s >= x and e <= y) {
    flag[ind] += val;
    seg[ind] += val;
    return;
  }
  relax(s, e, ind);
  int mid = (s + e) / 2;
  add(s, mid, ((ind)*2), x, y, val);
  add(mid, e, (((ind)*2) + 1), x, y, val);
  update(s, e, ind);
}
int main() {
  ios::sync_with_stdio(false);
  cin >> n >> m >> h;
  for (int i = 0; i < m; i++) cin >> b[i];
  sort(b, b + m);
  reverse(b, b + m);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    k[i] = calc(a[i]);
  }
  for (int i = 0; i < m; i++) add(0, m, 1, i, i + 1, 0);
  for (int i = 0; i < m; i++) add(0, m, 1, 0, k[i] + 1, 1);
  int ans = 0;
  if (seg[1] >= 1) ans++;
  for (int i = m; i < n; i++) {
    add(0, m, 1, 0, k[i - m] + 1, -1);
    add(0, m, 1, 0, k[i] + 1, 1);
    if (seg[1] >= 1) ans++;
  }
  cout << ans << endl;
  return 0;
}
