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 = 150005;
struct Node {
  int left, right, add, mn;
} L[N << 2];
int n, h, b[N], len, a[N];
void bulid(int step, int l, int r) {
  L[step].left = l;
  L[step].right = r;
  L[step].add = 0;
  L[step].mn = 0;
  if (l == r) return;
  int m = (l + r) >> 1;
  bulid(step << 1, l, m);
  bulid(step << 1 | 1, m + 1, r);
}
void update(int step, int l, int r, int v);
void push_down(int step) {
  int l = L[step].left, r = L[step].right, m = (l + r) >> 1;
  if (L[step].add) {
    update(step << 1, l, m, L[step].add);
    update(step << 1 | 1, m + 1, r, L[step].add);
    L[step].add = 0;
  }
}
void push_up(int step) {
  L[step].mn = min(L[step << 1].mn, L[step << 1 | 1].mn);
}
void update(int step, int l, int r, int v) {
  if (L[step].left == l && L[step].right == r) {
    L[step].mn += v;
    L[step].add += v;
    return;
  }
  push_down(step);
  int m = (L[step].left + L[step].right) >> 1;
  if (r <= m)
    update(step << 1, l, r, v);
  else if (l > m)
    update(step << 1 | 1, l, r, v);
  else {
    update(step << 1, l, m, v);
    update(step << 1 | 1, m + 1, r, v);
  }
  push_up(step);
}
int main() {
  int t;
  scanf("%d %d %d", &n, &len, &h);
  for (int i = 0; i < len; i++) scanf("%d", &b[i]);
  sort(b, b + len);
  bulid(1, 0, len);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    a[i] = lower_bound(b, b + len, h - a[i]) - b;
  }
  for (int i = 0; i < len; i++) update(1, i, i, -(i + 1));
  for (int i = 0; i < len - 1; i++) update(1, a[i], len, 1);
  int ans = 0;
  for (int i = len - 1; i < n; i++) {
    update(1, a[i], len, 1);
    if (L[1].mn >= 0) ans++;
    update(1, a[i - len + 1], len, -1);
  }
  printf("%d\n", ans);
  return 0;
}
