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 = 150005;
int sum[maxn << 2], add[maxn << 2];
int n, m, h;
int a[maxn], b[maxn];
void down(int rt) {
  if (add[rt]) {
    add[rt << 1] += add[rt];
    add[rt << 1 | 1] += add[rt];
    sum[rt << 1] += add[rt];
    sum[rt << 1 | 1] += add[rt];
    add[rt] = 0;
  }
}
void update(int L, int R, int v, int l = 1, int r = m, int rt = 1) {
  if (L <= l && r <= R) {
    sum[rt] += v;
    add[rt] += v;
    return;
  }
  int mid = (l + r) >> 1;
  down(rt);
  if (L <= mid) update(L, R, v, l, mid, rt << 1);
  if (R > mid) update(L, R, v, mid + 1, r, rt << 1 | 1);
  sum[rt] = min(sum[rt << 1], sum[rt << 1 | 1]);
}
void print(int l = 1, int r = m, int rt = 1) {
  if (l == r) {
    printf("%d ", sum[rt]);
    return;
  }
  down(rt);
  int mid = (l + r) >> 1;
  print(l, mid, rt << 1);
  print(mid + 1, r, rt << 1 | 1);
}
void debug() {
  print();
  puts("~~~~~");
}
int ans;
int main() {
  int i;
  scanf("%d%d%d", &n, &m, &h);
  for (i = 0; i < m; i++) scanf("%d", &b[i]);
  sort(b, b + m);
  for (i = 0; i < m; i++) update(i + 1, m, -1);
  for (i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    a[i] = lower_bound(b, b + m, h - a[i]) - b;
    if (a[i] < m) update(a[i] + 1, m, 1);
    if (i >= m && a[i - m] < m) update(a[i - m] + 1, m, -1);
    if (i >= m - 1) ans += sum[1] >= 0;
  }
  printf("%d\n", ans);
  return 0;
}
