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 inf = 1e9;
const int N = 200000;
int a[N], b[N];
int n, m, h;
int ma[4 * N], add[4 * N];
bool cmp(int a, int b) { return a > b; }
void pushdown(int x) {
  add[x + x] += add[x];
  add[x + x + 1] += add[x];
  add[x] = 0;
}
void pushup(int x) {
  ma[x] = (ma[x + x] + add[x + x] > ma[x + x + 1] + add[x + x + 1]
               ? ma[x + x] + add[x + x]
               : ma[x + x + 1] + add[x + x + 1]);
}
void insert(int x, int l, int r, int tl, int tr, int v) {
  if (l > tr || r < tl) return;
  if (l <= tl && r >= tr) {
    add[x] += v;
    return;
  }
  pushdown(x);
  int mid = (tr + tl) / 2;
  insert(x * 2, l, r, tl, mid, v);
  insert(x * 2 + 1, l, r, mid + 1, tr, v);
  pushup(x);
}
int main() {
  scanf("%d%d%d", &n, &m, &h);
  for (int i = 1; i <= m; i++) scanf("%d", b + i);
  sort(b + 1, b + m + 1, cmp);
  for (int i = 1; i <= n; i++) {
    int tmp;
    scanf("%d", &tmp);
    int l = 1, r = m + 1;
    while (r != l) {
      int mid = (l + r) >> 1;
      if (b[mid] + tmp >= h)
        l = mid + 1;
      else
        r = mid;
    }
    l--;
    a[i] = l;
  }
  for (int i = 0; i <= m; i++) insert(1, i, i, 0, m, -i);
  for (int i = 1; i <= m; i++) insert(1, a[i], m, 0, m, 1);
  int ans = 0;
  for (int i = m; i <= n; i++) {
    if ((ma[1] + add[1]) <= 0) ans++;
    if (i != n) {
      insert(1, a[i - m + 1], m, 0, m, -1);
      insert(1, a[i + 1], m, 0, m, 1);
    }
  }
  printf("%d\n", ans);
  return 0;
}
