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;
const int maxN = 150005;
int n, m, h;
struct Tnode {
  int id, val, maxV, add;
  Tnode *f, *son[2];
} tree[maxN], *root, *nul;
int s[maxN], c[maxN], r[maxN];
int trees;
Tnode *newnode(int id, int val) {
  trees++;
  tree[trees].id = id;
  tree[trees].val = tree[trees].maxV = val;
  tree[trees].son[0] = tree[trees].son[1] = tree[trees].f = nul;
  return tree + trees;
}
void updata(Tnode *root) {
  root->maxV = root->val;
  if (root->son[0] != nul) root->maxV = max(root->maxV, root->son[0]->maxV);
  if (root->son[1] != nul) root->maxV = max(root->maxV, root->son[1]->maxV);
}
void down(Tnode *root) {
  if (root->add == 0) return;
  if (root->son[0] != nul) {
    root->son[0]->add += root->add;
    root->son[0]->val += root->add;
    root->son[0]->maxV += root->add;
  }
  if (root->son[1] != nul) {
    root->son[1]->add += root->add;
    root->son[1]->val += root->add;
    root->son[1]->maxV += root->add;
  }
  root->add = 0;
}
void Readln() {
  scanf("%d%d%d\n", &n, &m, &h);
  for (int i = 1; i <= m; i++) {
    int val;
    scanf("%d", &val);
    r[i] = h - val;
  }
  for (int i = 1; i <= n; i++) scanf("%d", &s[i]);
}
bool cmp(int a, int b) { return a > b; }
void rot(Tnode *u, int t) {
  Tnode *v = u->f, *w = v->f;
  if (w != nul) {
    if (w->son[0] == v) w->son[0] = u;
    if (w->son[1] == v) w->son[1] = u;
  }
  u->f = w;
  v->son[t ^ 1] = u->son[t];
  if (u->son[t] != nul) u->son[t]->f = v;
  v->f = u;
  u->son[t] = v;
  updata(v);
}
void splay(Tnode *u, Tnode *fa) {
  while (u->f != fa && u->f != nul) {
    Tnode *v = u->f;
    Tnode *w = v->f;
    down(w);
    down(v);
    down(u);
    if (w == nul) {
      rot(u, v->son[0] == u);
      break;
    }
    bool p = (v->son[0] == u), q = (w->son[0] == v);
    if (p ^ q) {
      rot(u, p);
      rot(u, q);
    } else {
      rot(v, q);
      rot(u, p);
    }
  }
  if (fa == nul) root = u;
}
Tnode *findpred(int id) {
  Tnode *now = root, *ret = nul;
  while (now != nul) {
    down(now);
    if (now->id >= id) {
      ret = now;
      now = now->son[1];
    } else
      now = now->son[0];
  }
  return ret;
}
Tnode *inittree(Tnode *fa, int lef, int rig) {
  if (lef > rig) return nul;
  int mid = (lef + rig) / 2;
  Tnode *now = newnode(r[c[mid]], c[mid]);
  now->f = fa;
  if (lef == rig) return now;
  now->son[0] = inittree(now, lef, mid - 1);
  now->son[1] = inittree(now, mid + 1, rig);
  updata(now);
  return now;
}
void addtree(int id, int val) {
  Tnode *pre = findpred(id + 1);
  if (pre == nul) {
    root->add += val;
    root->maxV += val;
    root->val += val;
    return;
  }
  splay(pre, nul);
  if (root->son[1] == nul) return;
  root->son[1]->add += val;
  root->son[1]->maxV += val;
  root->son[1]->val += val;
  updata(root);
}
void Solve() {
  sort(r + 1, r + 1 + m, cmp);
  int tm = 0;
  for (int i = 1; i <= m; i++)
    if (r[i] != r[i + 1] && r[i] > 0) {
      tm++;
      c[tm] = i;
    }
  nul = newnode(0, -1000000);
  root = inittree(nul, 1, tm);
  for (int i = 1; i <= m; i++) addtree(s[i], -1);
  int ans = 0;
  if (root->maxV <= 0) ans++;
  for (int i = m + 1; i <= n; i++) {
    addtree(s[i - m], 1);
    addtree(s[i], -1);
    if (root->maxV <= 0) ans++;
  }
  printf("%d\n", ans);
}
int main() {
  Readln();
  Solve();
  return 0;
}
