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 Maxn = 150005;
int n, len, h, ans = 0;
int a[Maxn], b[Maxn];
inline int get() {
  char ch;
  while (!isdigit(ch = getchar()))
    ;
  int v = ch - 48;
  while (isdigit(ch = getchar())) v = v * 10 + ch - 48;
  return v;
}
struct node {
  int sum, mins;
  node *lc, *rc, *fa;
  void update() {
    sum = lc->sum + rc->sum;
    mins = min(lc->mins + rc->sum, rc->mins);
  }
} po[Maxn * 2], *pn = po;
class Segment_Tree {
  node *root, *p[Maxn];
  void build(node *&x, int l, int r) {
    x = ++pn;
    if (l == r) {
      p[l] = x;
      x->sum = x->mins = -1;
      return;
    }
    int mid = (l + r) >> 1;
    build(x->lc, l, mid);
    x->lc->fa = x;
    build(x->rc, mid + 1, r);
    x->rc->fa = x;
    x->update();
  }

 public:
  void build() { build(root, 1, len); }
  void modify(int pos, int c) {
    if (pos == 0) return;
    node *x = p[pos];
    x->sum += c;
    x->mins += c;
    for (x = x->fa; x; x = x->fa) x->update();
  }
  int getans() { return root->mins; }
} tr;
int main() {
  n = get();
  len = get();
  h = get();
  for (int i = 1; i <= len; i++) b[i] = h - get();
  sort(b + 1, b + len + 1);
  for (int i = 1; i <= n; i++)
    a[i] = upper_bound(b + 1, b + len + 1, get()) - b - 1;
  tr.build();
  for (int i = 1; i <= len; i++) tr.modify(a[i], 1);
  ans = tr.getans() == 0;
  for (int i = 2; i + len - 1 <= n; i++)
    tr.modify(a[i - 1], -1), tr.modify(a[i + len - 1], 1),
        ans += tr.getans() == 0;
  printf("%d\n", ans);
  return 0;
}
