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;
int N, Len, H, Ans;
int A[155555], B[155555];
int L[4 * 155555], R[4 * 155555], Val[4 * 155555], Add[4 * 155555];
void up(int d) { Val[d] = min(Val[d << 1], Val[d << 1 | 1]); }
void down(int d) {
  int ld = d << 1, rd = d << 1 | 1;
  if (Add[d]) {
    Add[ld] += Add[d];
    Add[rd] += Add[d];
    Val[ld] += Add[d];
    Val[rd] += Add[d];
    Add[d] = 0;
  }
}
void build(int l, int r, int d) {
  L[d] = l;
  R[d] = r;
  if (l == r)
    Val[d] = l - Len - 1;
  else {
    int mid = (l + r) >> 1;
    build(l, mid, d << 1);
    build(mid + 1, r, d << 1 | 1);
    up(d);
  }
}
void update(int l, int r, int d, int v) {
  if (L[d] >= l && R[d] <= r) {
    Add[d] += v;
    Val[d] += v;
  } else {
    down(d);
    int mid = (L[d] + R[d]) >> 1;
    if (l <= mid) update(l, r, d << 1, v);
    if (r > mid) update(l, r, d << 1 | 1, v);
    up(d);
  }
}
int main() {
  cin >> N >> Len >> H;
  for (int l = 1; l <= Len; ++l) {
    cin >> B[l];
    B[l] = H - B[l];
  }
  sort(B + 1, B + Len + 1);
  for (int n = 1; n <= N; ++n) {
    cin >> A[n];
    A[n] = lower_bound(B + 1, B + Len + 1, A[n] + 1) - B - 1;
  }
  build(1, Len, 1);
  for (int n = 1; n <= N; ++n) {
    if (n > Len && A[n - Len]) update(1, A[n - Len], 1, -1);
    if (A[n]) update(1, A[n], 1, 1);
    if (Val[1] >= 0) ++Ans;
  }
  cout << Ans << endl;
  return 0;
}
