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>
const int N = 150005;
namespace SGT {
int add[N << 2], need[N << 2];
void build(int l, int r, int o) {
  add[o] = 0;
  need[o] = r;
  if (l == r) return;
  int m = l + r >> 1;
  build(l, m, o << 1);
  build(m + 1, r, o << 1 | 1);
}
void down(int o) {
  if (add[o]) {
    need[o << 1] -= add[o];
    need[o << 1 | 1] -= add[o];
    add[o << 1] += add[o];
    add[o << 1 | 1] += add[o];
    add[o] = 0;
  }
}
void update(int l, int r, int o, int L, int R, int val) {
  if (L <= l && r <= R) {
    need[o] -= val;
    add[o] += val;
  } else {
    int m = l + r >> 1;
    down(o);
    if (L <= m) update(l, m, o << 1, L, R, val);
    if (R > m) update(m + 1, r, o << 1 | 1, L, R, val);
    need[o] = std::max(need[o << 1], need[o << 1 | 1]);
  }
}
}  // namespace SGT
struct Node {
  int a[N], n;
  void push_back(int x) { a[n++] = x; }
  void Sort() { std::sort(a, a + n); }
  int operator[](int x) { return std::lower_bound(a, a + n, x) - a + 1; }
} ly;
int a[N];
int main() {
  int n, len, h;
  scanf("%d%d%d", &n, &len, &h);
  for (int i = 0; i < len; i++) {
    int x;
    scanf("%d", &x);
    ly.push_back(x);
  }
  ly.Sort();
  SGT::build(1, len, 1);
  int ans = 0;
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    int pos = ly[std::max(h - a[i], 1)];
    if (pos <= ly.n) SGT::update(1, len, 1, pos, len, 1);
    if (i >= len - 1) {
      ans += (SGT::need[1] == 0);
      pos = ly[std::max(h - a[i - len + 1], 1)];
      if (pos <= ly.n) SGT::update(1, len, 1, pos, len, -1);
    }
  }
  printf("%d\n", ans);
  return 0;
}
