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;
int a[200000], b[200000];
struct node {
  int st, ed, flag, mn;
} mem[200000 * 3];
void Push_up(int u) {
  mem[u].mn = min(mem[(u << 1)].mn, mem[((u << 1) + 1)].mn);
}
void Make_Tree(int u, int st, int ed, int m) {
  mem[u].st = st;
  mem[u].ed = ed;
  mem[u].flag = 0;
  if (ed == st + 1) {
    mem[u].mn = st - m;
    return;
  }
  Make_Tree((u << 1), st, ((st + ed) >> 1), m);
  Make_Tree(((u << 1) + 1), ((st + ed) >> 1), ed, m);
  Push_up(u);
}
void Push_down(int u) {
  if (mem[u].flag == 0) return;
  mem[(u << 1)].flag += mem[u].flag;
  mem[((u << 1) + 1)].flag += mem[u].flag;
  mem[(u << 1)].mn += mem[u].flag;
  mem[((u << 1) + 1)].mn += mem[u].flag;
  mem[u].flag = 0;
}
void update(int u, int st, int ed, int add) {
  st = max(mem[u].st, st);
  ed = min(mem[u].ed, ed);
  if (st >= ed) return;
  if (st == mem[u].st && ed == mem[u].ed) {
    mem[u].flag += add;
    mem[u].mn += add;
    return;
  }
  Push_down(u);
  update((u << 1), st, ed, add);
  update(((u << 1) + 1), st, ed, add);
  Push_up(u);
}
int main() {
  int n, m, h;
  cin >> n >> m >> h;
  for (int i = 0; i < m; i++) scanf("%d", b + i), b[i] = h - b[i];
  for (int i = 0; i < n; i++) scanf("%d", a + i);
  sort(b, b + m);
  int ans = 0;
  Make_Tree(1, 0, m, m);
  for (int i = 0, j = 0; i <= n - m; i++) {
    while (j < i + m) {
      int pos = upper_bound(b, b + m, a[j]) - b;
      if (pos) update(1, 0, pos, 1);
      j++;
    }
    if (mem[1].mn >= 0) ans++;
    int pos = upper_bound(b, b + m, a[i]) - b;
    if (pos) update(1, 0, pos, -1);
  }
  cout << ans << endl;
  return 0;
}
