Manao is solving a problem with the following statement:

<image>

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;
template <typename T, typename S>
ostream &operator<<(ostream &os, const pair<T, S> &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <typename C, typename T = decay<decltype(*begin(declval<C>()))>,
          typename enable_if<!is_same<C, string>::value>::type * = nullptr>
ostream &operator<<(ostream &os, const C &c) {
  bool f = true;
  os << "[";
  for (const auto &x : c) {
    if (!f) os << ", ";
    f = false;
    os << x;
  }
  return os << "]";
}
template <typename T>
void debug(string s, T x) {
  cerr << s << " = " << x << "\n";
}
template <typename T, typename... Args>
void debug(string s, T x, Args... args) {
  for (int i = 0, b = 0; i < (int)s.size(); i++)
    if (s[i] == '(' || s[i] == '{')
      b++;
    else if (s[i] == ')' || s[i] == '}')
      b--;
    else if (s[i] == ',' && b == 0) {
      cerr << s.substr(0, i) << " = " << x << " | ";
      debug(s.substr(s.find_first_not_of(' ', i + 1)), args...);
      break;
    }
}
struct SegmentTree {
  int n;
  vector<int> a, st, lazy;
  SegmentTree(int _n) : n(_n), st(4 * n), lazy(4 * n) {}
  SegmentTree(const vector<int> &_a)
      : n((int)_a.size()), a(_a), st(4 * n), lazy(4 * n) {
    build(1, 0, n - 1);
  }
  void build(int p, int l, int r) {
    if (l == r) {
      st[p] = a[l];
      return;
    }
    int m = (l + r) / 2;
    build(2 * p, l, m);
    build(2 * p + 1, m + 1, r);
    st[p] = max(st[2 * p], st[2 * p + 1]);
  }
  void push(int p, int l, int r) {
    if (lazy[p]) {
      st[p] += lazy[p];
      if (l != r) {
        lazy[2 * p] += lazy[p];
        lazy[2 * p + 1] += lazy[p];
      }
      lazy[p] = 0;
    }
  }
  int query(int p, int l, int r, int i, int j) {
    push(p, l, r);
    if (i > r || j < l) return INT_MIN;
    if (i <= l && r <= j) return st[p];
    int m = (l + r) / 2;
    return max(query(2 * p, l, m, i, j), query(2 * p + 1, m + 1, r, i, j));
  }
  int query(int i, int j) { return query(1, 0, n - 1, i, j); }
  void update(int p, int l, int r, int i, int j, int val) {
    push(p, l, r);
    if (i > r || j < l) return;
    if (i <= l && r <= j) {
      st[p] += val;
      if (l != r) {
        lazy[2 * p] += val;
        lazy[2 * p + 1] += val;
      }
      return;
    }
    int m = (l + r) / 2;
    update(2 * p, l, m, i, j, val);
    update(2 * p + 1, m + 1, r, i, j, val);
    st[p] = max(st[2 * p], st[2 * p + 1]);
  }
  void update(int i, int j, int val) { update(1, 0, n - 1, i, j, val); }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, len, h;
  cin >> n >> len >> h;
  vector<int> a(n), b(len);
  for (int i = 0; i < len; i++) cin >> b[i];
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(b.rbegin(), b.rend());
  SegmentTree st(len + 1);
  for (int i = 1; i <= len; i++) st.update(i, i, -i);
  int ret = 0;
  vector<int> pos(n);
  for (int i = 0; i < n; i++) {
    pos[i] = int(upper_bound(b.begin(), b.end(), h - a[i], greater<int>()) -
                 b.begin());
    st.update(pos[i], len, 1);
    if (i >= len - 1) {
      if (st.st[1] == 0) ret++;
      st.update(pos[i - len + 1], len, -1);
    }
  }
  cout << ret << "\n";
  return 0;
}
