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 = 150000 + 5, INF = 1000000000 + 1;
int n, m, h, i, res, q[N], a[N], b[N];
int ma[4 * N], t[4 * N];
int min(int x, int y) {
  if (x < y) return x;
  return y;
}
void update(int v, int tl, int tr, int pos, int de) {
  int tm;
  if (tl == tr) {
    ma[v] += de;
    t[v] += de;
    return;
  }
  tm = (tl + tr) >> 1;
  if (pos <= tm)
    update(v + v, tl, tm, pos, de);
  else
    update(v + v + 1, tm + 1, tr, pos, de);
  t[v] = t[v + v] + t[v + v + 1];
  ma[v] = min(ma[v + v], t[v + v] + ma[v + v + 1]);
}
int BS(int k) {
  int s = 1, f = m, md, re = 0;
  while (s <= f) {
    md = (s + f) / 2;
    if (b[md] <= k) {
      s = md + 1;
      re = md;
    } else
      f = md - 1;
  }
  return re;
}
int CH() {
  if (ma[1] >= 0) return 1;
  return 0;
}
int main() {
  scanf("%d%d%d", &n, &m, &h);
  for (i = 1; i <= m; ++i) {
    scanf("%d", &b[i]);
  }
  for (i = 1; i <= n; ++i) {
    scanf("%d", &a[i]);
  }
  for (i = 1; i <= m; ++i) {
    b[i] = h - b[i];
  }
  sort(b + 1, b + m + 1);
  for (i = 1; i <= n; ++i) {
    q[i] = BS(a[i]);
    q[i] = m + 1 - q[i];
  }
  for (i = 1; i <= m; ++i) {
    update(1, 1, m + 1, i, -1);
    update(1, 1, m + 1, q[i], 1);
  }
  res += CH();
  for (i = m + 1; i <= n; ++i) {
    update(1, 1, m + 1, q[i - m], -1);
    update(1, 1, m + 1, q[i], 1);
    res += CH();
  }
  printf("%d\n", res);
  return 0;
}
