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;
typedef int arr32[1000010];
arr32 g, e, v, a, q, d;
int n, h, len, ans;
void build(int k, int l, int r) {
  if (l == r) {
    v[k] = g[l];
    return;
  }
  build((k << 1), l, ((l + r) >> 1));
  build((k << 1) + 1, ((l + r) >> 1) + 1, r);
  v[k] = max(v[(k << 1)], v[(k << 1) + 1] + e[(k << 1)]);
}
void modify(int k, int l, int r, int x, int z) {
  e[k] += z;
  if (l == r) {
    v[k] += z;
    return;
  }
  if (x <= ((l + r) >> 1))
    modify((k << 1), l, ((l + r) >> 1), x, z);
  else
    modify((k << 1) + 1, ((l + r) >> 1) + 1, r, x, z);
  v[k] = max(v[(k << 1)], v[(k << 1) + 1] + e[(k << 1)]);
}
bool cmp(const int &x, const int &y) { return a[x] < a[y]; }
int main() {
  scanf("%d %d %d", &n, &len, &h);
  for (int i = 1; i <= len; ++i) {
    scanf("%d", a + i + n);
    a[i + n] = h - a[i + n] - 1;
    q[i + n] = i + n;
  }
  sort(a + n + 1, a + n + len + 1);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", a + i);
    q[i] = i;
  }
  sort(q + 1, q + n + len + 1, cmp);
  int vt = 1;
  for (int i = 1; i <= n + len; ++i) {
    d[q[i]] = i;
    if (q[i] > n) {
      for (int j = vt; j <= i; ++j) g[j] -= q[i] - n;
      vt = i + 1;
    }
  }
  for (int i = vt; i <= n + len; ++i) g[i] -= len + 3;
  build(1, 1, n + len);
  for (int i = 1; i <= len; ++i) modify(1, 1, n + len, d[i], 1);
  ans += v[1] < 0;
  for (int i = len + 1; i <= n; ++i) {
    modify(1, 1, n + len, d[i - len], -1);
    modify(1, 1, n + len, d[i], 1);
    ans += v[1] < 0;
  }
  printf("%d", ans);
}
