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 = 100 * 100 * 100;
int mn[4 * MAXN + 10];
int marked[4 * MAXN + 10];
void update(int node, int b, int e, int p, int q, int val) {
  if (marked[node] != 0) {
    marked[2 * node] += marked[node];
    marked[2 * node + 1] += marked[node];
    mn[2 * node] += marked[node];
    mn[2 * node + 1] += marked[node];
    marked[node] = 0;
  }
  if (p <= b && q >= e) {
    marked[node] += val;
    mn[node] += val;
    return;
  }
  if (p > e || q < b) return;
  update(2 * node, b, (b + e) / 2, p, q, val);
  update(2 * node + 1, (b + e) / 2 + 1, e, p, q, val);
  mn[node] = min(mn[2 * node], mn[2 * node + 1]);
}
int query(int node, int b, int e, int p) {
  if (marked[node] != 0) {
    marked[2 * node] += marked[node];
    marked[2 * node + 1] += marked[node];
    mn[2 * node] += marked[node];
    mn[2 * node + 1] += marked[node];
    marked[node] = 0;
  }
  if (b == e) return mn[node];
  if (p <= (b + e) / 2)
    return query(2 * node, b, (b + e) / 2, p);
  else
    return query(2 * node + 1, (b + e) / 2 + 1, e, p);
}
int n, len, h;
vector<int> A;
int a[MAXN + 10];
int main() {
  cin >> n >> len >> h;
  for (int i = 1; i <= len; i++) {
    int q;
    cin >> q;
    A.push_back(q);
  }
  sort(A.begin(), A.end());
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= len; i++) update(1, 1, MAXN, i, i, len - i + 1);
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    if (i > len) {
      int pos = lower_bound(A.begin(), A.end(), h - a[i - len]) - A.begin() + 1;
      update(1, 1, MAXN, 1, pos, 1);
    }
    int pos = lower_bound(A.begin(), A.end(), h - a[i]) - A.begin() + 1;
    update(1, 1, MAXN, 1, pos, -1);
    if (i >= len && mn[1] == 0) ans++;
  }
  cout << ans << endl;
  return 0;
}
