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>
const int Maxn = 150005;
int n, len, h, a[Maxn], b[Maxn], pos[Maxn];
struct node {
  int l, r, val, lazy;
} Tree[4 * Maxn];
void build(int l, int r, int ind) {
  Tree[ind].l = l, Tree[ind].r = r, Tree[ind].lazy = 0, Tree[ind].val = -r;
  if (l != r) {
    int mid = (l + r) >> 1;
    build(l, mid, ((ind) << 1));
    build(mid + 1, r, (((ind) << 1) | 1));
  }
}
void add(int l, int r, int val, int ind) {
  int ll = Tree[ind].l, rr = Tree[ind].r, mid = (ll + rr) >> 1;
  if (l <= ll && r >= rr) {
    Tree[ind].val += val, Tree[ind].lazy += val;
    return;
  }
  if (Tree[ind].lazy != 0) {
    add(ll, mid, Tree[ind].lazy, ((ind) << 1));
    add(mid + 1, rr, Tree[ind].lazy, (((ind) << 1) | 1));
    Tree[ind].lazy = 0;
  }
  if (l <= mid) add(l, r, val, ((ind) << 1));
  if (r > mid) add(l, r, val, (((ind) << 1) | 1));
  Tree[ind].val = ((Tree[((ind) << 1)].val) < (Tree[(((ind) << 1) | 1)].val)
                       ? (Tree[((ind) << 1)].val)
                       : (Tree[(((ind) << 1) | 1)].val));
}
void init() {
  scanf("%d%d%d", &n, &len, &h);
  for (int i = 1; i <= len; i++) scanf("%d", &b[i]);
  std::sort(b + 1, b + len + 1);
  build(1, len, 1);
}
void slove() {
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    pos[i] = -1;
    if (a[i] + b[len] >= h) {
      int l = 1, r = len, mid;
      while (l < r) {
        mid = (l + r) >> 1;
        if (a[i] + b[mid] >= h)
          r = mid;
        else
          l = mid + 1;
      }
      pos[i] = r;
    }
    if (pos[i] != -1) add(pos[i], len, 1, 1);
    if (i > len && pos[i - len] != -1) add(pos[i - len], len, -1, 1);
    if (Tree[1].val >= 0) ans++;
  }
  printf("%d\n", ans);
}
int main() {
  init();
  slove();
  return 0;
}
