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 = 3e5 + 20, inf = 1e17;
long long n, len, h, tmp, A[maxn], B[maxn], seg[4 * maxn], lazy[4 * maxn], ans;
vector<long long> V;
map<long long, long long> mp;
void shift(long long id) {
  seg[2 * id] += lazy[id];
  seg[2 * id + 1] += lazy[id];
  lazy[2 * id] += lazy[id];
  lazy[2 * id + 1] += lazy[id];
  lazy[id] = 0;
}
void upd(long long s, long long e, long long id, long long l, long long r,
         long long val) {
  if (s >= l && e <= r) {
    seg[id] += val;
    lazy[id] += val;
    return;
  }
  if (s >= r || e <= l) return;
  shift(id);
  long long mid = (s + e) / 2;
  upd(s, mid, id * 2, l, r, val);
  upd(mid, e, id * 2 + 1, l, r, val);
  seg[id] = min(seg[id * 2], seg[id * 2 + 1]);
}
int32_t main() {
  cin >> n >> len >> h;
  for (long long i = 0; i < len; i++) {
    cin >> tmp;
    B[i] = h - tmp;
    V.push_back(B[i]);
  }
  for (long long i = 0; i < n; i++) {
    cin >> A[i];
    V.push_back(A[i]);
  }
  sort(V.begin(), V.end());
  mp[V[0]] = 1;
  tmp = 2;
  for (long long i = 1; i < V.size(); i++) {
    if (V[i] != V[i - 1]) {
      mp[V[i]] = tmp;
      tmp++;
    }
  }
  for (long long i = 0; i < len; i++) {
    upd(0, maxn, 1, 0, mp[B[i]], -1);
    upd(0, maxn, 1, 0, mp[A[i]], 1);
  }
  for (long long i = 0; i < n - len + 1; i++) {
    if (seg[1] == 0) ans++;
    upd(0, maxn, 1, 0, mp[A[i]], -1);
    upd(0, maxn, 1, 0, mp[A[i + len]], 1);
  }
  cout << ans;
}
