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 = 5e5 + 7;
int n, m, f[N];
int maxn[N], flag[N];
void ad(int id, int x) { maxn[id] += x, flag[id] += x; }
void pushdown(int id) {
  if (flag[id]) ad(id << 1, flag[id]), ad(id << 1 | 1, flag[id]), flag[id] = 0;
}
void upd(int id) { maxn[id] = max(maxn[id << 1], maxn[id << 1 | 1]); }
void add(int id, int L, int R, int l, int r, int val) {
  if (l <= L && R <= r) return ad(id, val), void();
  int mid = (L + R) / 2;
  pushdown(id);
  if (l <= mid) add(id << 1, L, mid, l, r, val);
  if (r > mid) add(id << 1 | 1, mid + 1, R, l, r, val);
  upd(id);
}
int upper(int x) {
  int L = 1, R = m, ans = m + 1;
  while (L <= R) {
    int mid = (L + R) / 2;
    if (f[mid] >= x)
      R = mid - 1, ans = mid;
    else
      L = mid + 1;
  }
  return ans;
}
int h, a[N];
int main() {
  scanf("%d%d%d", &n, &m, &h);
  for (int i = 1, iE = m; i <= iE; i++) scanf("%d", &f[i]);
  sort(f + 1, f + m + 1);
  for (int i = 1, iE = m; i <= iE; i++) add(1, 1, m, i, i, i);
  for (int i = 1, iE = n; i <= iE; i++) scanf("%d", &a[i]);
  for (int i = 1, iE = m - 1; i <= iE; i++) {
    int k = upper(h - a[i]);
    if (k <= m) add(1, 1, m, k, m, -1);
  }
  int cnt = 0;
  for (int i = 1, iE = n - m + 1; i <= iE; i++) {
    int k = upper(h - a[i + m - 1]);
    if (k <= m) add(1, 1, m, k, m, -1);
    if (maxn[1] == 0) ++cnt;
    k = upper(h - a[i]);
    if (k <= m) add(1, 1, m, k, m, 1);
  }
  printf("%d\n", cnt);
  return 0;
}
