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 long long INF = (long long)1e18 + 123;
const int inf = (int)2e9 + 123;
const int mod = 1e9 + 7;
using namespace std;
int a[150011], b[150011], t[1000011], add[1000011], n, h, length;
void push(int v, int tl, int tr) {
  if (add[v] == 0) return;
  t[v] += add[v];
  if (tl < tr) {
    add[v * 2] += add[v];
    add[v * 2 + 1] += add[v];
  }
  add[v] = 0;
}
void build(int v = 1, int tl = 1, int tr = length) {
  if (tl == tr) {
    t[v] = -(length - tl + 1);
    return;
  }
  int tm = (tl + tr) / 2;
  build(v * 2, tl, tm);
  build(v * 2 + 1, tm + 1, tr);
  t[v] = min(t[v * 2], t[v * 2 + 1]);
}
void upd(int l, int r, int x, int v = 1, int tl = 1, int tr = length) {
  push(v, tl, tr);
  if (tl > r || tr < l || l > r) return;
  if (tl >= l && tr <= r) {
    add[v] += x;
    push(v, tl, tr);
    return;
  }
  int tm = (tl + tr) / 2;
  upd(l, r, x, v * 2, tl, tm);
  upd(l, r, x, v * 2 + 1, tm + 1, tr);
  t[v] = min(t[v * 2], t[v * 2 + 1]);
}
int get(int x) {
  int l = 1, r = length, mx = 0;
  while (l <= r) {
    int tm = (l + r) / 2;
    if (x + b[tm] >= h) {
      mx = tm;
      l = tm + 1;
    } else
      r = tm - 1;
  }
  return mx;
}
int main() {
  unsigned int FOR;
  asm("rdtsc" : "=A"(FOR));
  srand(FOR);
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> length >> h;
  for (int i = 1; i <= length; i++) {
    cin >> b[i];
  }
  sort(b + 1, b + 1 + length);
  reverse(b + 1, b + 1 + length);
  build();
  for (int i = 1; i <= length; i++) {
    cin >> a[i];
    upd(1, get(a[i]), 1);
  }
  int ans = 0;
  if (t[1] >= 0) ans++;
  for (int i = length + 1; i <= n; i++) {
    upd(1, get(a[i - length]), -1);
    cin >> a[i];
    upd(1, get(a[i]), 1);
    if (t[1] >= 0) ans++;
  }
  cout << ans;
  return 0;
}
