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>
using namespace std;
const int MAXN = 1500015;
int seg[1 << 20];
int tmp[1 << 20];
int a[MAXN], b[MAXN];
void build(int id, int lo, int hi) {
  if (lo == hi) {
    seg[id] = -lo;
    return;
  }
  int mid = lo + hi;
  mid /= 2;
  build(id * 2, lo, mid);
  build(id * 2 + 1, mid + 1, hi);
  seg[id] = -hi;
}
void query(int val, int s, int e, int lo, int hi, int id) {
  if (s > hi || e < lo) return;
  if (s <= lo && hi <= e) {
    seg[id] += val;
    tmp[id] += val;
    return;
  }
  int mid = (lo + hi) / 2;
  query(val, s, e, lo, mid, id * 2);
  query(val, s, e, mid + 1, hi, id * 2 + 1);
  seg[id] = tmp[id] + min(seg[id * 2 + 1], seg[id * 2]);
}
int main() {
  int h, n, len;
  cin >> n >> len >> h;
  for (int i = 0; i < len; i++) {
    cin >> b[i];
  }
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  sort(b, b + len);
  build(1, 0, len - 1);
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    query(1, (lower_bound(b, b + len, h - a[i]) - b), len - 1, 0, len - 1, 1);
    if (i + 1 >= len) {
      if (seg[1] > 0) ans++;
      query(-1, (lower_bound(b, b + len, h - a[i - len + 1]) - b), len - 1, 0,
            len - 1, 1);
    }
  }
  cout << ans;
}
