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 U>
std::istream& operator>>(std::istream& i, pair<T, U>& p) {
  i >> p.first >> p.second;
  return i;
}
template <typename T>
std::istream& operator>>(std::istream& i, vector<T>& t) {
  for (auto& v : t) {
    i >> v;
  }
  return i;
}
template <typename T, typename U>
std::ostream& operator<<(std::ostream& o, const pair<T, U>& p) {
  o << p.first << ' ' << p.second;
  return o;
}
template <typename T>
std::ostream& operator<<(std::ostream& o, const vector<T>& t) {
  if (t.empty()) o << '\n';
  for (size_t i = 0; i < t.size(); ++i) {
    o << t[i] << " \n"[i == t.size() - 1];
  }
  return o;
}
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T, vector<T>, less<T>>;
template <typename T>
bool in(T a, T b, T c) {
  return a <= b && b < c;
}
unsigned int logceil(int first) {
  return 8 * sizeof(int) - __builtin_clz(first);
}
namespace std {
template <typename T, typename U>
struct hash<pair<T, U>> {
  hash<T> t;
  hash<U> u;
  size_t operator()(const pair<T, U>& p) const {
    return t(p.first) ^ (u(p.second) << 7);
  }
};
}  // namespace std
template <typename T, typename F>
T bsh(T l, T h, const F& f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      l = m + 1;
      r = m;
    } else {
      h = m - 1;
    }
  }
  return r;
}
template <typename F>
double bshd(double l, double h, const F& f, double p = 1e-9) {
  unsigned int r = 3 + (unsigned int)log2((h - l) / p);
  while (r--) {
    double m = (l + h) / 2;
    if (f(m)) {
      l = m;
    } else {
      h = m;
    }
  }
  return (l + h) / 2;
}
template <typename T, typename F>
T bsl(T l, T h, const F& f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      h = m - 1;
      r = m;
    } else {
      l = m + 1;
    }
  }
  return r;
}
template <typename F>
double bsld(double l, double h, const F& f, double p = 1e-9) {
  unsigned int r = 3 + (unsigned int)log2((h - l) / p);
  while (r--) {
    double m = (l + h) / 2;
    if (f(m)) {
      h = m;
    } else {
      l = m;
    }
  }
  return (l + h) / 2;
}
template <typename T>
T gcd(T a, T b) {
  if (a < b) swap(a, b);
  return b ? gcd(b, a % b) : a;
}
template <typename T>
class vector2 : public vector<vector<T>> {
 public:
  vector2() {}
  vector2(size_t a, size_t b, T t = T())
      : vector<vector<T>>(a, vector<T>(b, t)) {}
};
template <typename T>
class vector3 : public vector<vector2<T>> {
 public:
  vector3() {}
  vector3(size_t a, size_t b, size_t c, T t = T())
      : vector<vector2<T>>(a, vector2<T>(b, c, t)) {}
};
template <typename T>
class vector4 : public vector<vector3<T>> {
 public:
  vector4() {}
  vector4(size_t a, size_t b, size_t c, size_t d, T t = T())
      : vector<vector3<T>>(a, vector3<T>(b, c, d, t)) {}
};
template <typename T>
class vector5 : public vector<vector4<T>> {
 public:
  vector5() {}
  vector5(size_t a, size_t b, size_t c, size_t d, size_t e, T t = T())
      : vector<vector4<T>>(a, vector4<T>(b, c, d, e, t)) {}
};
template <typename F>
struct NoOp {
  void setup(unsigned int, F) {}
  void op(F& p, F n, unsigned int, unsigned int) { p = n; }
  void down(F&, F&, F&, unsigned int, unsigned int) {}
};
template <typename F, typename SetOp, typename PowerOp>
struct Lazy {
  void setup(unsigned int s, F def) {
    this->def = def;
    this->s = s;
    L = new F[s]();
    fill(L, L + s, def);
  }
  void down(F& u, F& l, F& r, unsigned int i, unsigned int s) {
    op(l, L[i], i << 1, s >> 1);
    op(r, L[i], i << 1 | 1, s >> 1);
    L[i] = def;
  }
  void op(F& p, F n, unsigned int i, unsigned int s) {
    p = sop(p, pop(n, s));
    if (i < this->s) this->L[i] = sop(this->L[i], n);
  }
  SetOp sop;
  PowerOp pop;
  F* L;
  unsigned int s;
  F def;
};
template <typename F, typename CombineOp, typename ModifyOp = NoOp<F>>
struct SegTree {
  void setup(unsigned int s, F def) {
    n = 1 << logceil(s);
    T = vector<F>(2 * n, def);
    for (unsigned int i = n - 1; i > 0; i--)
      T[i] = cop(T[i << 1], T[i << 1 | 1]);
    mop.setup(2 * n, def);
  }
  void setup(vector<F>& data, F def = F()) {
    n = 1 << logceil(data.size());
    T = vector<F>(2 * n, def);
    copy(data.begin(), data.end(), T.begin() + n);
    for (unsigned int i = n - 1; i > 0; i--)
      T[i] = cop(T[i << 1], T[i << 1 | 1]);
    mop.setup(2 * n, def);
  }
  inline void put(unsigned int first, F n) { put(first, first, n); }
  inline void put(unsigned int from, unsigned int to, F v) {
    put2(from, to + 1, v, 1, n);
  }
  inline F get(unsigned int first) { return get(first, first); }
  inline F get(unsigned int from, unsigned int to) {
    return get2(from, to + 1, 1, n);
  }
  void put2(unsigned int from, unsigned int to, F v, unsigned int i,
            unsigned int s) {
    if (from == 0 && to == s) {
      mop.op(T[i], v, i, s);
      return;
    }
    mop.down(T[i], T[i << 1], T[i << 1 | 1], i, s);
    s >>= 1;
    i <<= 1;
    if (to <= s) {
      put2(from, to, v, i, s);
    } else if (from >= s) {
      put2(from - s, to - s, v, i | 1, s);
    } else {
      put2(from, s, v, i, s);
      put2(0, to - s, v, i | 1, s);
    }
    T[i >> 1] = cop(T[i], T[i | 1]);
  }
  F get2(unsigned int from, unsigned int to, unsigned int i, unsigned int s) {
    while (true) {
      if (from == 0 && to == s) return T[i];
      mop.down(T[i], T[i << 1], T[i << 1 | 1], i, s);
      s >>= 1;
      i <<= 1;
      if (to > s) {
        to -= s;
        if (from >= s) {
          from -= s;
          i |= 1;
        } else
          return cop(get2(from, s, i, s), get2(0, to, i | 1, s));
      }
    }
  }
  unsigned int n;
  vector<F> T;
  CombineOp cop;
  ModifyOp mop;
};
template <typename F>
struct AddOp {
  F operator()(F a, F b) { return a + b; }
};
template <typename F>
struct MinOp {
  F operator()(F a, F b) { return std::min(a, b); }
};
template <typename F>
struct MaxOp {
  F operator()(F a, F b) { return std::max(a, b); }
};
template <typename F>
struct MultiplyOp {
  F operator()(F a, F b) { return a * b; }
};
template <typename F>
struct MultOp {
  F operator()(F a, unsigned int b) { return a * b; }
};
template <typename F>
struct IdempOp {
  F operator()(F a, unsigned int b) { return a; }
};
template <typename F>
struct InverseOp {
  F operator()(F a, F b) { return b ? b - a : a; }
};
template <typename T>
using AddSumTree = SegTree<T, AddOp<T>, Lazy<T, AddOp<T>, MultOp<T>>>;
template <typename T>
using AddMaxTree = SegTree<T, MaxOp<T>, Lazy<T, AddOp<T>, IdempOp<T>>>;
template <typename T>
using AddMinTree = SegTree<T, MinOp<T>, Lazy<T, AddOp<T>, IdempOp<T>>>;
template <typename T>
using AssignMinTree = SegTree<T, MinOp<T>, Lazy<T, MinOp<T>, IdempOp<T>>>;
template <typename T>
using AssignMaxTree = SegTree<T, MaxOp<T>, Lazy<T, MaxOp<T>, IdempOp<T>>>;
template <typename T>
using XorTree = SegTree<T, AddOp<T>, Lazy<T, InverseOp<T>, MultOp<T>>>;
template <typename T>
using SetMinTree = SegTree<T, MinOp<T>>;
template <typename T>
using SetMaxTree = SegTree<T, MaxOp<T>>;
template <typename T>
using SetMulTree = SegTree<T, MultiplyOp<T>>;
class optimize {
 public:
  void solve(istream& cin, ostream& cout) {
    int N, Len, H;
    cin >> N >> Len >> H;
    vector<int> B(Len), A(N);
    cin >> B >> A;
    set<int> C;
    C.insert(0);
    C.insert(H);
    for (int& a : A) {
      a = min(a, H);
      C.insert(H - a);
    }
    for (int& b : B) {
      b = min(b, H);
      if (b) {
        C.insert(b - 1);
        C.insert(b);
      }
    }
    map<int, int> W;
    int S = 0;
    for (auto it = C.begin(); it != C.end(); ++S, ++it) W[*it] = S;
    AddMinTree<int> T;
    T.setup(S, 0);
    for (int b : B)
      if (b) T.put(0, W[b - 1], 1);
    for (int i = 0; i < Len - 1; ++i) T.put(W[H - A[i]], S - 1, 1);
    int ans = 0;
    for (int j = Len - 1; j < A.size(); ++j) {
      T.put(W[H - A[j]], W[H], 1);
      ans += (T.get(0, S - 1) >= Len);
      T.put(W[H - A[j - Len + 1]], S - 1, -1);
    }
    cout << ans << endl;
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  optimize solver;
  std::istream& in(std::cin);
  std::ostream& out(std::cout);
  solver.solve(in, out);
  return 0;
}
