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>
const int N = 150000 + 9;
int a[N], min[N * 4], tag[N * 4], b[N], n, len, h, L, R, D;
inline void push_up(const int idx) {
  min[idx] = std::min(min[idx * 2], min[idx * 2 + 1]);
}
inline void push_down(const int idx) {
  if (!tag[idx]) return;
  tag[idx * 2] += tag[idx];
  tag[idx * 2 + 1] += tag[idx];
  min[idx * 2] += tag[idx];
  min[idx * 2 + 1] += tag[idx];
  tag[idx] = 0;
}
void modify(const int idx, const int l, const int r) {
  if (L <= l && r <= R) return (void)(min[idx] += D, tag[idx] += D);
  const int mid = (l + r) / 2;
  if (tag[idx]) push_down(idx);
  if (L <= mid) modify(idx * 2, l, mid);
  if (mid < R) modify(idx * 2 + 1, mid + 1, r);
  push_up(idx);
}
int main() {
  scanf("%d%d%d", &n, &len, &h);
  for (int i = 1; i <= len; ++i) {
    scanf("%d", b + i);
    L = R = i;
    D = len - i + 1;
    modify(1, 1, len);
  }
  for (int i = 1; i <= n; ++i) {
    scanf("%d", a + i);
    a[i] = h - a[i];
  }
  std::sort(b + 1, b + 1 + len);
  int cnt = 0, ans = 0;
  for (int i = 1; i <= len; ++i) {
    if (a[i] > b[len]) {
      ++cnt;
      continue;
    }
    if (i != 1 && a[i] <= 0) continue;
    L = 1;
    R = std::lower_bound(b + 1, b + 1 + len, a[i]) - b;
    D = -1;
    modify(1, 1, len);
  }
  if (!cnt && min[1] >= 0) ++ans;
  for (int i = len + 1; i <= n; ++i) {
    if (a[i - len] <= b[len]) {
      L = 1;
      R = std::lower_bound(b + 1, b + 1 + len, a[i - len]) - b;
      D = 1;
      modify(1, 1, len);
    } else
      --cnt;
    if (a[i - len + 1] <= 0) {
      L = 1;
      R = std::lower_bound(b + 1, b + 1 + len, a[i - len + 1]) - b;
      D = -1;
      modify(1, 1, len);
    }
    if (a[i] > b[len]) {
      ++cnt;
      continue;
    }
    if (a[i] > 0) {
      L = 1;
      R = std::lower_bound(b + 1, b + 1 + len, a[i]) - b;
      D = -1;
      modify(1, 1, len);
    }
    if (!cnt && min[1] >= 0) ++ans;
  }
  printf("%d\n", ans);
}
