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 int maxn = 600005, maxk = maxn << 2;
int n, len, h, ans;
int a[maxn], b[maxn], pos[maxn], lc[maxk], rc[maxk], minn[maxk], lazy[maxk];
inline int cmp(int a, int b) { return a > b; }
inline void pushup(int now) { minn[now] = min(minn[lc[now]], minn[rc[now]]); }
inline void getlazy(int now, int v) { lazy[now] += v, minn[now] += v; }
inline void pushdown(int now) {
  if (lazy[now] == 0) return;
  getlazy(lc[now], lazy[now]), getlazy(rc[now], lazy[now]);
  lazy[now] = 0;
}
void build(int l, int r, int now) {
  if (l == r) {
    minn[now] = -(len - l + 1);
    return;
  }
  int mid = (l + r) >> 1;
  lc[now] = now << 1, rc[now] = now << 1 | 1;
  build(l, mid, lc[now]), build(mid + 1, r, rc[now]);
  pushup(now);
}
void update(int l, int r, int now, int L, int R, int v) {
  if (L > R || now == 0) return;
  if (L <= l && r <= R) {
    getlazy(now, v);
    return;
  }
  int mid = (l + r) >> 1;
  pushdown(now);
  if (L <= mid) update(l, mid, lc[now], L, R, v);
  if (mid < R) update(mid + 1, r, rc[now], L, R, v);
  pushup(now);
}
int main() {
  scanf("%d%d%d", &n, &len, &h);
  for (int i = 1; i <= len; i++) scanf("%d", &b[i]);
  sort(b + 1, b + 1 + len, cmp);
  build(1, len, 1);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    int l = 0, r = len + 1;
    while (l + 1 < r) {
      int mid = (l + r) >> 1;
      if (a[i] + b[mid] >= h)
        l = mid;
      else
        r = mid;
    }
    pos[i] = l;
    update(1, len, 1, 1, pos[i], 1);
    if (i >= len) {
      ans += (minn[1] >= 0);
      update(1, len, 1, 1, pos[i - len + 1], -1);
    }
  }
  printf("%d\n", ans);
  return 0;
}
