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 + 6.66;
const int inf = 1e9 + 7;
int seg[MAXN * 4], laz[MAXN * 4];
int a[MAXN], b[MAXN];
int n, m, h;
void shift(int id, int val) {
  seg[id] += val;
  laz[id] += val;
}
void shift(int id) {
  shift(id << 1, laz[id]);
  shift(id << 1 | 1, laz[id]);
  laz[id] = 0;
}
void build(int id, int l, int r) {
  if (l >= r) return;
  if (r - l == 1) {
    seg[id] = -l - 1;
    return;
  }
  int mid = l + (r - l) / 2;
  build(id << 1, l, mid);
  build(id << 1 | 1, mid, r);
  seg[id] = min(seg[id << 1], seg[id << 1 | 1]);
}
void alter(int id, int l, int r, int b, int e, int val) {
  if (l >= r) return;
  if (l >= e || r <= b) return;
  if (l >= b && r <= e) {
    seg[id] += val;
    laz[id] += val;
    return;
  }
  shift(id);
  int mid = (l + r) >> 1;
  alter(id << 1, l, mid, b, e, val);
  alter(id << 1 | 1, mid, r, b, e, val);
  seg[id] = min(seg[id << 1], seg[id << 1 | 1]);
}
int get(int id, int l, int r, int b, int e) {
  if (l >= r) return inf;
  if (l >= e || r <= b) return inf;
  if (l >= b && r <= e) return seg[id];
  shift(id);
  int mid = (l + r) >> 1;
  return min(get(id << 1, l, mid, b, e), get(id << 1 | 1, mid, r, b, e));
}
void rem(int val) {
  int f = h - a[val];
  int pos = lower_bound(b, b + m, f) - b;
  if (pos < m) alter(1, 0, m, pos, m, -1);
}
void add(int val) {
  int f = h - a[val];
  int pos = lower_bound(b, b + m, f) - b;
  if (pos < m) alter(1, 0, m, pos, m, 1);
}
int get_min() { return get(1, 0, m, 0, m); }
int main() {
  cin >> n >> m >> h;
  for (int i = 0; i < m; i++) cin >> b[i];
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(b, b + m);
  build(1, 0, m);
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (i >= m) rem(i - m);
    add(i);
    if (get_min() >= 0) ans++;
  }
  cout << ans << endl;
  return 0;
}
