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 N = 2e5 + 100;
const long long int mod = 1e9 + 7;
const int inf = 1e8;
int n, m, h, ans = 0;
vector<int> b;
long long int p[N], mn[4 * N], lazy[4 * N];
void upd(int ind) {
  lazy[ind * 2] += lazy[ind];
  mn[ind * 2] += lazy[ind];
  lazy[ind * 2 + 1] += lazy[ind];
  mn[ind * 2 + 1] += lazy[ind];
  lazy[ind] = 0;
  return;
}
void add(int l, int r, int val, int b = 0, int e = m + 1, int ind = 1) {
  if (e <= l || b >= r) return;
  upd(ind);
  if (l <= b && e <= r) {
    mn[ind] += val;
    lazy[ind] += val;
    return;
  }
  int mid = (b + e) / 2;
  add(l, r, val, b, mid, ind * 2);
  add(l, r, val, mid, e, ind * 2 + 1);
  mn[ind] = min(mn[ind * 2], mn[ind * 2 + 1]);
  return;
}
void build(int b = 0, int e = m + 1, int ind = 1) {
  if (b + 1 == e) {
    mn[ind] = m - b;
    return;
  }
  int mid = (b + e) / 2;
  build(b, mid, ind * 2);
  build(mid, e, ind * 2 + 1);
  mn[ind] = min(mn[ind * 2], mn[ind * 2 + 1]);
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cin >> n >> m >> h;
  for (int i = 0; i < m; i++) {
    int k;
    cin >> k;
    b.push_back(k);
  }
  sort(b.begin(), b.end());
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    a -= h;
    p[i] = lower_bound(b.begin(), b.end(), -a) - b.begin();
  }
  build();
  for (int i = 0; i < m - 1; i++) add(0, p[i] + 1, -1);
  for (int i = m - 1; i < n; i++) {
    add(0, p[i] + 1, -1);
    if (mn[1] >= 0) ans++;
    add(0, p[i - m + 1] + 1, 1);
  }
  cout << ans << endl;
  return 0;
}
