One day, ZS the Coder wrote down an array of integers a with elements a1, a2, ..., an.

A subarray of the array a is a sequence al, al + 1, ..., ar for some integers (l, r) such that 1 ≤ l ≤ r ≤ n. ZS the Coder thinks that a subarray of a is beautiful if the bitwise xor of all the elements in the subarray is at least k.

Help ZS the Coder find the number of beautiful subarrays of a!

Input

The first line contains two integers n and k (1 ≤ n ≤ 106, 1 ≤ k ≤ 109) — the number of elements in the array a and the value of the parameter k.

The second line contains n integers ai (0 ≤ ai ≤ 109) — the elements of the array a.

Output

Print the only integer c — the number of beautiful subarrays of the array a.

Examples

Input

3 1
1 2 3


Output

5


Input

3 2
1 2 3


Output

3


Input

3 3
1 2 3


Output

2
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int INF = 1000000000;
const ll LINF = 1001002003004005006ll;
int dx[] = {1, 0, -1, 0}, dy[] = {0, 1, 0, -1};
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
struct IOSetup {
  IOSetup() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(12);
  }
} iosetup;
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++)
    os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &x : v) is >> x;
  return is;
}
template <typename T, int MAX_LOG>
struct BinaryTrie {
 public:
  struct Node {
    Node *nxt[2];
    ll ch_cnt;
    Node() : nxt{nullptr, nullptr}, ch_cnt(0) {}
  };
  Node *root;
  BinaryTrie() : root(new Node()) {}
  BinaryTrie(Node *root) : root(root) {}
  void add(const T &bit, int idx = -1, ll cnt = 1, T xor_val = 0) {
    root = add(root, bit, idx, MAX_LOG, cnt, xor_val);
  }
  void erase(const T &bit, T xor_val = 0) { add(bit, -1, -1, xor_val); }
  Node *find(const T &bit, T xor_val = 0) {
    return find(root, bit, MAX_LOG, xor_val);
  }
  ll count(const T &bit, T xor_val = 0) {
    auto node = find(bit, xor_val);
    return node ? node->ch_cnt : 0;
  }
  pair<T, Node *> min_element(T xor_val = 0) {
    assert(root->ch_cnt > 0);
    return kth_element(0, xor_val);
  }
  pair<T, Node *> max_element(T xor_val = 0) {
    assert(root->ch_cnt > 0);
    return kth_element(root->ch_cnt - 1, xor_val);
  }
  pair<T, Node *> kth_element(ll k, T xor_val = 0) {
    assert(0 <= k and k < root->ch_cnt);
    return kth_element(root, k, MAX_LOG, xor_val);
  }
  ll count_less(const T &bit, T xor_val = 0) {
    return count_less(root, bit, MAX_LOG, xor_val);
  }

 private:
  virtual Node *clone(Node *t) { return t; }
  Node *add(Node *t, T bit, int idx, int depth, ll x, T xor_val,
            bool need = true) {
    if (need) t = clone(t);
    if (depth == -1) {
      t->ch_cnt += x;
    } else {
      bool f = (xor_val >> depth) & 1;
      auto &to = t->nxt[f ^ ((bit >> depth) & 1)];
      if (!to) to = new Node(), need = false;
      to = add(to, bit, idx, depth - 1, x, xor_val, need);
      t->ch_cnt += x;
    }
    return t;
  }
  Node *find(Node *t, T bit, int depth, T xor_val) {
    if (depth == -1)
      return t;
    else {
      bool f = (xor_val >> depth) & 1;
      auto &to = t->nxt[f ^ ((bit >> depth) & 1)];
      return to ? find(to, bit, depth - 1, xor_val) : nullptr;
    }
  }
  pair<T, Node *> kth_element(Node *t, ll k, int depth, T xor_val) {
    if (depth == -1)
      return {0, t};
    else {
      bool f = (xor_val >> depth) & 1;
      if ((t->nxt[f] ? t->nxt[f]->ch_cnt : 0) <= k) {
        auto ret =
            kth_element(t->nxt[f ^ 1], k - (t->nxt[f] ? t->nxt[f]->ch_cnt : 0),
                        depth - 1, xor_val);
        ret.first |= T(1) << depth;
        return ret;
      } else
        return kth_element(t->nxt[f], k, depth - 1, xor_val);
    }
  }
  ll count_less(Node *t, const T &bit, int depth, T xor_val) {
    if (depth == -1) return 0;
    ll ret = 0;
    bool f = (xor_val >> depth) & 1;
    if ((bit >> depth) & 1) {
      if (t->nxt[f]) ret += t->nxt[f]->ch_cnt;
      if (t->nxt[f ^ 1])
        ret += count_less(t->nxt[f ^ 1], bit, depth - 1, xor_val);
    } else {
      if (t->nxt[f]) ret += count_less(t->nxt[f], bit, depth - 1, xor_val);
    }
    return ret;
  }
};
signed main() {
  ll n, k;
  cin >> n >> k;
  vector<int> a(n);
  cin >> a;
  vector<int> s(n + 1);
  s[0] = 0;
  for (int i = 0; i < (n); i++) s[i + 1] = (s[i] ^ a[i]);
  BinaryTrie<int, 30> trie;
  vector<ll> naive;
  ll res = 0;
  for (int i = 0; i < (n + 1); i++) {
    res += trie.count_less(k, s[i]);
    trie.add(s[i]);
  }
  cout << n * (n + 1) / 2 - res << endl;
  return 0;
}
