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 long long Maxn = 2e5 + 7;
const long long Max = 5e5 + 7;
long long n, len, h, ans;
long long b[Maxn], a[Maxn];
long long suf[Maxn];
long long sum[Maxn * 4], ted[Maxn * 4];
void dsu() {
  for (long long i = 1; i <= n; i++)
    suf[i] = lower_bound(b + 1, b + len + 1, h - a[i]) - b;
}
void update_top(long long node) {
  ted[2 * node] += ted[node];
  ted[2 * node + 1] += ted[node];
  sum[2 * node] += ted[node];
  sum[2 * node + 1] += ted[node];
  ted[node] = 0;
}
void update_down(long long node) {
  sum[node] = min(sum[2 * node], sum[2 * node + 1]);
}
void make(long long l, long long r, long long node = 1) {
  if (l == r) {
    sum[node] = -l;
    return;
  }
  long long mid = (l + r) / 2;
  make(l, mid, 2 * node);
  make(mid + 1, r, 2 * node + 1);
  update_down(node);
}
void add(long long l, long long r, long long st, long long X,
         long long node = 1) {
  if (st > len + 1 || r < st) return;
  if (st <= l) {
    sum[node] += X;
    ted[node] += X;
    return;
  }
  long long mid = (l + r) / 2;
  update_top(node);
  add(l, mid, st, X, 2 * node);
  add(mid + 1, r, st, X, 2 * node + 1);
  update_down(node);
}
void Find() {
  if (sum[1] >= 0) ans++;
}
void Solve() {
  for (long long i = 1; i <= len; i++) add(1, len, suf[i], +1);
  Find();
  for (long long i = len + 1; i <= n; i++) {
    add(1, len, suf[i - len], -1);
    add(1, len, suf[i], +1);
    Find();
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> len >> h;
  for (long long i = 1; i <= len; i++) cin >> b[i];
  for (long long i = 1; i <= n; i++) cin >> a[i];
  sort(b + 1, b + len + 1);
  dsu();
  make(1, len);
  Solve();
  cout << ans << endl;
  return 0;
}
