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 = 150100;
int n, len, h;
int a[N], b[N];
struct Seg {
  bool ok;
  int num;
  int add;
} seg[N << 2];
void push_up(int rt) {
  seg[rt].ok = seg[rt << 1].ok & seg[rt << 1 | 1].ok;
  seg[rt].num = min(seg[rt << 1].num, seg[rt << 1 | 1].num);
}
void build(int l, int r, int rt) {
  seg[rt].add = 0;
  if (l == r) {
    seg[rt].num = -l;
    seg[rt].ok = false;
    return;
  }
  int m = (l + r) >> 1;
  build(l, m, rt << 1);
  build(m + 1, r, rt << 1 | 1);
  push_up(rt);
}
void maintain(int rt, int v) {
  seg[rt].num += v;
  seg[rt].add += v;
  if (seg[rt].num >= 0)
    seg[rt].ok = true;
  else
    seg[rt].ok = false;
}
void push_down(int rt) {
  maintain(rt << 1, seg[rt].add);
  maintain(rt << 1 | 1, seg[rt].add);
  seg[rt].add = 0;
}
void update(int L, int R, int v, int l, int r, int rt) {
  if (L <= l && r <= R) {
    maintain(rt, v);
    return;
  }
  push_down(rt);
  int m = (l + r) >> 1;
  if (L <= m) update(L, R, v, l, m, rt << 1);
  if (R > m) update(L, R, v, m + 1, r, rt << 1 | 1);
  push_up(rt);
}
int main() {
  ios::sync_with_stdio(false);
  cin >> n >> len >> h;
  for (int i = 1; i <= len; i++) cin >> b[i];
  for (int i = 1; i <= n; i++) cin >> a[i];
  sort(b + 1, b + len + 1);
  build(1, len, 1);
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    int x = h - a[i];
    int pos = lower_bound(b + 1, b + len + 1, x) - b;
    if (pos <= len) update(pos, len, 1, 1, len, 1);
    if (i - len >= 1) {
      x = h - a[i - len];
      pos = lower_bound(b + 1, b + len + 1, x) - b;
      if (pos <= len) update(pos, len, -1, 1, len, 1);
    }
    if (seg[1].ok) ans++;
  }
  cout << ans << endl;
  return 0;
}
