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;
#pragma comment(linker, "/STACK:64000000")
const int maxn = 1 << 18;
const int inf = 1000000007;
const int mod = 1000000007;
int n, len, h;
int a[maxn], b[maxn];
int t[2 * maxn], add[2 * maxn];
void push(int v, int tl, int tr) {
  if (add[v]) {
    if (tl != tr) add[v * 2] += add[v];
    if (tl != tr) add[v * 2 + 1] += add[v];
    t[v] += add[v];
    add[v] = 0;
  }
}
void upd(int v, int tl, int tr, int l, int r, int x) {
  push(v, tl, tr);
  if (l > r) return;
  if (l == tl && r == tr) {
    add[v] += x;
    push(v, tl, tr);
    return;
  }
  int tm = (tl + tr) >> 1;
  upd(v * 2, tl, tm, l, min(r, tm), x);
  upd(v * 2 + 1, tm + 1, tr, max(l, tm + 1), r, x);
  t[v] = min(t[v * 2], t[v * 2 + 1]);
}
int main() {
  while (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);
    for (int i = 0; i < len; i++) upd(1, 0, len - 1, i, i, -i - 1);
    for (int i = 0; i < len; i++)
      upd(1, 0, len - 1, lower_bound(b, b + len, h - a[i]) - b, len - 1, 1);
    int ans = 0;
    for (int i = 0; i + len - 1 < n; i++) {
      ans += t[1] >= 0;
      upd(1, 0, len - 1, lower_bound(b, b + len, h - a[i]) - b, len - 1, -1);
      upd(1, 0, len - 1, lower_bound(b, b + len, h - a[i + len]) - b, len - 1,
          1);
    }
    cout << ans << endl;
  }
  return 0;
}
