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 N = 150500;
const int inf = 1e9;
inline int read() {
  char ch;
  while ((ch = getchar()) < '0' || ch > '9')
    ;
  int res = ch - '0';
  while ((ch = getchar()) >= '0' && ch <= '9') res = res * 10 + ch - '0';
  return res;
}
int H, n, len, tag[N << 2], mn[N << 2];
int a[N], b[N];
void pushup(int k) { mn[k] = min(mn[k << 1], mn[k << 1 | 1]) + tag[k]; }
void chg(int k, int v) {
  tag[k] += v;
  mn[k] += v;
}
void modify(int k, int l, int r, int x, int y, int v) {
  if (l >= x && r <= y) return chg(k, v);
  if (l > y || r < x) return;
  int mid = l + r >> 1;
  modify(k << 1, l, mid, x, y, v);
  modify(k << 1 | 1, mid + 1, r, x, y, v);
  pushup(k);
}
int main() {
  n = read();
  len = read();
  H = read();
  for (int i = 1; i <= len; i++) b[i] = read();
  sort(b + 1, b + 1 + len);
  for (int i = 1; i <= n; i++) {
    a[i] = read();
    a[i] = lower_bound(b + 1, b + 1 + len, H - a[i]) - b;
  }
  int ans = 0;
  for (int i = 1; i <= len; i++) modify(1, 1, len, i, len, -1);
  for (int i = 1; i <= len; i++) modify(1, 1, len, a[i], len, 1);
  if (mn[1] >= 0) ans++;
  for (int i = len + 1; i <= n; i++) {
    modify(1, 1, len, a[i - len], len, -1);
    modify(1, 1, len, a[i], len, 1);
    if (mn[1] >= 0) ans++;
  }
  printf("%d", ans);
  return 0;
}
