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 = 15e4 + 10;
int n, a[N], b[N], len, h, data[4 * N], flag[4 * N], ans, compress;
map<int, int> com;
vector<int> all;
void shift(int node) {
  if (flag[node] == 0) return;
  data[node * 2 + 0] += flag[node];
  data[node * 2 + 1] += flag[node];
  flag[node * 2 + 0] += flag[node];
  flag[node * 2 + 1] += flag[node];
  flag[node] = 0;
}
void add(int node, int st, int en, int l, int r, int val) {
  if (en <= l or r <= st) return;
  if (l <= st and en <= r) {
    flag[node] += val;
    data[node] += val;
    return;
  }
  int mid = (st + en) / 2;
  shift(node);
  add(node * 2 + 0, st, mid, l, r, val);
  add(node * 2 + 1, mid, en, l, r, val);
  data[node] = min(data[node * 2 + 0], data[node * 2 + 1]);
}
int get(int node, int st, int en, int l, int r) {
  if (en <= l or r <= st) return 0;
  if (l <= st and en <= r) return data[node];
  shift(node);
  int mid = (st + en) / 2;
  return min(get(node * 2 + 0, st, mid, l, r),
             get(node * 2 + 1, mid, en, l, r));
}
int main() {
  cin >> n >> len >> h;
  for (int i = 0; i < len; ++i) cin >> b[i];
  for (int i = 0; i < n; ++i) cin >> a[i], all.push_back(a[i]);
  for (int i = 0; i < len; ++i) b[i] = h - b[i], all.push_back(b[i]);
  compress = 1;
  sort(all.begin(), all.end());
  com[all[0]] = compress;
  for (int i = 1; i < all.size(); ++i)
    if (all[i] != all[i - 1]) com[all[i]] = ++compress;
  compress++;
  for (int i = 0; i < all.size(); ++i) all[i] = com[all[i]];
  for (int i = 0; i < n; ++i) a[i] = com[a[i]];
  for (int i = 0; i < len; ++i) b[i] = com[b[i]];
  for (int i = 0; i < len; ++i) add(1, 0, compress, 0, b[i] + 1, -1);
  for (int i = 0; i < len; ++i) add(1, 0, compress, 0, a[i] + 1, 1);
  if (get(1, 0, compress, 0, compress) > -1) ans++;
  for (int i = len; i < n; ++i) {
    add(1, 0, compress, 0, a[i - len] + 1, -1);
    add(1, 0, compress, 0, a[i] + 1, 1);
    if (get(1, 0, compress, 0, compress) > -1) ans++;
  }
  cout << ans;
}
