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 = 150010;
int seg[maxn << 2];
int mrk[maxn << 2];
int a[maxn];
int b[maxn];
int n, len, h;
void PushUP(int rt) { seg[rt] = min(seg[rt << 1], seg[rt << 1 | 1]); }
void build(int l, int r, int rt) {
  if (l == r) {
    mrk[rt] = 0;
    seg[rt] = l - len - 1;
    return;
  }
  mrk[rt] = 0;
  int m = (l + r) >> 1;
  build(l, m, rt << 1);
  build(m + 1, r, rt << 1 | 1);
  PushUP(rt);
}
void PushDown(int rt) {
  if (mrk[rt] != 0) {
    mrk[rt << 1] += mrk[rt];
    mrk[rt << 1 | 1] += mrk[rt];
    seg[rt << 1] += mrk[rt];
    seg[rt << 1 | 1] += mrk[rt];
    mrk[rt] = 0;
  }
}
void update(int L, int R, int c, int l, int r, int rt) {
  if (L <= l && r <= R) {
    mrk[rt] += c;
    seg[rt] += c;
    return;
  }
  PushDown(rt);
  int m = (l + r) >> 1;
  if (L <= m) update(L, R, c, l, m, rt << 1);
  if (R > m) update(L, R, c, m + 1, r, rt << 1 | 1);
  PushUP(rt);
}
int main() {
  std::ios_base::sync_with_stdio(false);
  cin >> n >> len >> h;
  for (int i = 0; i < len; i++) {
    int a;
    cin >> a;
    b[i] = h - a;
  }
  sort(b, b + len);
  int m = len;
  build(1, m, 1);
  int ans = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    int order = upper_bound(b, b + len, a[i]) - b;
    if (order > 0) update(1, order, 1, 1, m, 1);
    if (i >= len - 1) {
      if (seg[1] >= 0) ans++;
      order = upper_bound(b, b + len, a[i - len + 1]) - b;
      if (order > 0) update(1, order, -1, 1, m, 1);
    }
  }
  cout << ans << endl;
  return 0;
}
