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 maxn = 1.5e5 + 10;
int b[maxn], a[maxn];
int n, m, h;
int min_val[maxn << 2], add_val[maxn << 2];
void push_down(int o) {
  if (add_val[o]) {
    int lc = o << 1, rc = o << 1 | 1;
    add_val[lc] += add_val[o];
    add_val[rc] += add_val[o];
    min_val[lc] += add_val[o];
    min_val[rc] += add_val[o];
    add_val[o] = 0;
  }
}
void add(int L, int R, int x = 1, int l = 1, int r = m, int o = 1) {
  if (l >= L && r <= R) {
    add_val[o] += x;
    min_val[o] += x;
    return;
  }
  push_down(o);
  int mid = (l + r) >> 1;
  if (L <= mid) add(L, R, x, l, mid, o << 1);
  if (R > mid) add(L, R, x, mid + 1, r, o << 1 | 1);
  min_val[o] = min(min_val[o << 1], min_val[o << 1 | 1]);
}
int query(int L, int R, int l = 1, int r = m, int o = 1) {
  if (l >= l && r <= R) return min_val[o];
  push_down(o);
  int mid = (l + r) >> 1, ret = 0x3f3f3f3f;
  if (L <= mid) ret = min(query(L, R, l, mid, o << 1), ret);
  if (R > mid) ret = min(query(L, R, mid + 1, r, o << 1 | 1), ret);
  return ret;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> m >> h;
  for (int i = 1; i <= m; ++i) cin >> b[i];
  for (int i = 1; i <= n; ++i) cin >> a[i];
  sort(b + 1, b + m + 1);
  for (int i = 1; i <= m; ++i) add(i, i, -i);
  int ans = 0;
  for (int i = 1; i <= n; ++i) {
    int p = lower_bound(b + 1, b + m + 1, h - a[i]) - b;
    add(p, m);
    if (i >= m) {
      if (query(1, m) >= 0) ans++;
      int p = lower_bound(b + 1, b + m + 1, h - a[i - m + 1]) - b;
      add(p, m, -1);
    }
  }
  std::cout << ans << '\n';
  return 0;
}
