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 double eps = 1e-10;
const int N = 151000;
struct node {
  int l, r, del, add;
} t[N << 2];
int n, len, h, ans;
int a[N], b[N];
void update(int c) { t[c].del = min(t[c << 1].del, t[(c << 1) + 1].del); }
void pushdown(int c) {
  if (t[c].l + 1 == t[c].r || !t[c].add) return;
  t[c << 1].add += t[c].add;
  t[c << 1].del += t[c].add;
  t[(c << 1) + 1].add += t[c].add;
  t[(c << 1) + 1].del += t[c].add;
  t[c].add = 0;
}
void build(int c, int l, int r) {
  t[c].l = l, t[c].r = r;
  t[c].del = -r, t[c].add = 0;
  if (l + 1 >= r) return;
  int mid = (l + r) >> 1;
  build(c << 1, l, mid);
  build((c << 1) + 1, mid, r);
  update(c);
}
void modify(int c, int l, int r, int d) {
  pushdown(c);
  if (t[c].l == l && t[c].r == r) {
    t[c].add += d;
    t[c].del += d;
    return;
  }
  int mid = (t[c].l + t[c].r) >> 1;
  if (r <= mid)
    modify(c << 1, l, r, d);
  else if (l >= mid)
    modify((c << 1) + 1, l, r, d);
  else {
    modify(c << 1, l, mid, d);
    modify((c << 1) + 1, mid, r, d);
  }
  update(c);
}
int main() {
  scanf("%d%d%d", &n, &len, &h);
  for (int i = 0; i < len; ++i) scanf("%d", b + i);
  sort(b, b + len);
  for (int i = 0; i < n; ++i) {
    scanf("%d", a + i);
    a[i] = lower_bound(b, b + len, h - a[i]) - b;
  }
  build(1, 0, len);
  for (int i = 0; i < len; ++i)
    if (a[i] < len) modify(1, a[i], len, 1);
  if (t[1].del >= 0) ++ans;
  for (int i = len; i < n; ++i) {
    if (a[i - len] < len) modify(1, a[i - len], len, -1);
    if (a[i] < len) modify(1, a[i], len, 1);
    if (t[1].del >= 0) ++ans;
  }
  cout << ans << endl;
  return 0;
}
