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 v[160000];
int f[160000];
struct Node {
  int minv;
  int lazy;
} node[160000 << 2];
void app(int rt, int add) {
  node[rt].lazy += add;
  node[rt].minv += add;
}
void pushdown(int rt) {
  if (node[rt].lazy) {
    app(rt << 1, node[rt].lazy);
    app(rt << 1 | 1, node[rt].lazy);
    node[rt].lazy = 0;
  }
}
void pushup(int rt) {
  node[rt].minv = min(node[rt << 1].minv, node[rt << 1 | 1].minv);
}
void update(int rt, int L, int R, int l, int r, int add) {
  if (l <= L && r >= R) {
    app(rt, add);
  } else {
    pushdown(rt);
    if (l <= ((L + R) >> 1)) update(rt << 1, L, ((L + R) >> 1), l, r, add);
    if (r > ((L + R) >> 1))
      update(rt << 1 | 1, ((L + R) >> 1) + 1, R, l, r, add);
    pushup(rt);
  }
}
int main() {
  int n, m, h;
  int x;
  while (cin >> n >> m >> h) {
    memset(node, 0, sizeof(node));
    for (int i = 0; i < (m); ++i) {
      scanf("%d", &v[i]);
      f[i] = h - v[i];
    }
    sort(f, f + m);
    int len = unique(f, f + m) - f;
    f[len] = 2e9 + 10;
    len++;
    for (int i = 0; i < (m); ++i) {
      x = lower_bound(f, f + len - 1, h - v[i]) - f;
      update(1, 0, len - 1, 0, x, -1);
    }
    int ans = 0;
    for (int i = 0; i < (n); ++i) {
      scanf("%d", &v[i]);
      if (v[i] >= f[0]) {
        x = upper_bound(f, f + len - 1, v[i]) - f - 1;
        update(1, 0, len - 1, 0, x, 1);
      }
      if (i >= m && v[i - m] >= f[0]) {
        x = upper_bound(f, f + len - 1, v[i - m]) - f - 1;
        update(1, 0, len - 1, 0, x, -1);
      }
      if (i >= m - 1 && node[1].minv >= 0) ans++;
    }
    cout << ans << endl;
  }
  return 0;
}
