#include <bits/stdc++.h>
const int OO = 1;
const int inf = 2e9 + 7;
using namespace std;
string F[14];
int count(int i, string &s) {
  int rtn = 0;
  for (int st = 0; st + s.size() <= F[i].size(); st++) {
    bool found = true;
    for (int j = 0; found && j < s.size(); j++)
      if (s[j] != F[i][st + j]) found = false;
    if (found) rtn++;
  }
  return rtn;
}
vector<int> pref(int i, string &s) {
  vector<int> rtn;
  for (int en = 1; en <= s.size(); en++) {
    bool found = true;
    for (int sub = 1; found && en - sub >= 0; sub++)
      if (s[s.size() - sub] != F[i][en - sub]) found = false;
    if (found) rtn.push_back(en);
  }
  return rtn;
}
vector<int> suf(int i, string &s) {
  vector<int> rtn;
  for (int len = 1; len <= s.size(); len++) {
    bool found = true;
    for (int j = 0; found && j < len; j++)
      if (s[j] != F[i][F[i].size() - len + j]) found = false;
    if (found) rtn.push_back(len);
  }
  return rtn;
}
int n, m;
long long k;
long long C[202];
bool P[202][202];
bool S[202][202];
void calc(string &s) {
  vector<int> tmp;
  for (int len = 0; len <= s.size(); len++) P[12][len] = S[12][len] = 0;
  C[12] = count(12, s);
  tmp = pref(12, s);
  for (const auto &i : tmp) P[12][i] = 1;
  tmp = suf(12, s);
  for (const auto &i : tmp) S[12][i] = 1;
  for (int len = 0; len <= s.size(); len++) P[13][len] = S[13][len] = 0;
  C[13] = count(13, s);
  tmp = pref(13, s);
  for (const auto &i : tmp) P[13][i] = 1;
  tmp = suf(13, s);
  for (const auto &i : tmp) S[13][i] = 1;
  for (int i = 14; i <= n; i++) {
    C[i] = C[i - 2] + C[i - 1];
    for (int len = 1; len < s.size(); len++)
      if (S[i - 2][len] && P[i - 1][s.size() - len]) C[i]++;
    C[i] = min(C[i], k);
    for (int len = 0; len <= s.size(); len++) P[i][len] = P[i - 2][len];
    for (int len = 0; len <= s.size(); len++) S[i][len] = S[i - 1][len];
  }
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0);
  F[0] = "0";
  F[1] = "1";
  for (int i = 2; i < 14; i++) F[i] = F[i - 2] + F[i - 1];
  cin >> n >> k >> m;
  if (n < 14) {
    string ans = "", t0, t1;
    int c0, c1, cs0, cs1, len = 0;
    while (len < m) {
      len++;
      t0 = ans + '0';
      t1 = ans + '1';
      c0 = count(n, t0);
      c1 = count(n, t1);
      bool found;
      found = true;
      for (int i = 0; i < len; i++)
        if (t0[i] != F[n][F[n].size() - len + i]) found = false;
      cs0 = (found ? 1 : 0);
      found = true;
      for (int i = 0; i < len; i++)
        if (t1[i] != F[n][F[n].size() - len + i]) found = false;
      cs1 = (found ? 1 : 0);
      if (k <= cs0) {
        cout << (t0) << '\n', cin.ignore();
        cin.get();
        return 0;
      } else {
        k -= cs0;
        if (k <= c0)
          ans = t0;
        else {
          k -= c0;
          if (k <= cs1) {
            cout << (t1) << '\n', cin.ignore();
            cin.get();
            return 0;
          } else {
            k -= cs1;
            ans = t1;
          }
        }
      }
    }
    cout << (ans) << '\n', cin.ignore();
    cin.get();
    return 0;
  }
  string ans = "", t0, t1;
  long long c0, c1, cs0, cs1, len = 0;
  while (len < m) {
    len++;
    t0 = ans + '0';
    t1 = ans + '1';
    calc(t0);
    c0 = C[n];
    cs0 = S[n][len];
    calc(t1);
    c1 = C[n];
    cs1 = S[n][len];
    if (k <= cs0) {
      cout << (t0) << '\n', cin.ignore();
      cin.get();
      return 0;
    } else {
      k -= cs0;
      if (k <= c0)
        ans = t0;
      else {
        k -= c0;
        if (k <= cs1) {
          cout << (t1) << '\n', cin.ignore();
          cin.get();
          return 0;
        } else {
          k -= cs1;
          ans = t1;
        }
      }
    }
  }
  cout << ans << '\n';
  cin.ignore();
  cin.get();
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

Let's denote (yet again) the sequence of Fibonacci strings:

F(0) =  0, F(1) =  1, F(i) = F(i - 2) + F(i - 1), where the plus sign denotes the concatenation of two strings.

Let's denote the lexicographically sorted sequence of suffixes of string F(i) as A(F(i)). For example, F(4) is 01101, and A(F(4)) is the following sequence: 01, 01101, 1, 101, 1101. Elements in this sequence are numbered from 1.

Your task is to print m first characters of k-th element of A(F(n)). If there are less than m characters in this suffix, then output the whole suffix.

Input

The only line of the input contains three numbers n, k and m (1 ≤ n, m ≤ 200, 1 ≤ k ≤ 10^{18}) denoting the index of the Fibonacci string you have to consider, the index of the element of A(F(n)) and the number of characters you have to output, respectively.

It is guaranteed that k does not exceed the length of F(n).

Output

Output m first characters of k-th element of A(F(n)), or the whole element if its length is less than m.

Examples

Input

4 5 3


Output

110


Input

4 3 3


Output

1

### Response

```cpp
#include <bits/stdc++.h>
const int OO = 1;
const int inf = 2e9 + 7;
using namespace std;
string F[14];
int count(int i, string &s) {
  int rtn = 0;
  for (int st = 0; st + s.size() <= F[i].size(); st++) {
    bool found = true;
    for (int j = 0; found && j < s.size(); j++)
      if (s[j] != F[i][st + j]) found = false;
    if (found) rtn++;
  }
  return rtn;
}
vector<int> pref(int i, string &s) {
  vector<int> rtn;
  for (int en = 1; en <= s.size(); en++) {
    bool found = true;
    for (int sub = 1; found && en - sub >= 0; sub++)
      if (s[s.size() - sub] != F[i][en - sub]) found = false;
    if (found) rtn.push_back(en);
  }
  return rtn;
}
vector<int> suf(int i, string &s) {
  vector<int> rtn;
  for (int len = 1; len <= s.size(); len++) {
    bool found = true;
    for (int j = 0; found && j < len; j++)
      if (s[j] != F[i][F[i].size() - len + j]) found = false;
    if (found) rtn.push_back(len);
  }
  return rtn;
}
int n, m;
long long k;
long long C[202];
bool P[202][202];
bool S[202][202];
void calc(string &s) {
  vector<int> tmp;
  for (int len = 0; len <= s.size(); len++) P[12][len] = S[12][len] = 0;
  C[12] = count(12, s);
  tmp = pref(12, s);
  for (const auto &i : tmp) P[12][i] = 1;
  tmp = suf(12, s);
  for (const auto &i : tmp) S[12][i] = 1;
  for (int len = 0; len <= s.size(); len++) P[13][len] = S[13][len] = 0;
  C[13] = count(13, s);
  tmp = pref(13, s);
  for (const auto &i : tmp) P[13][i] = 1;
  tmp = suf(13, s);
  for (const auto &i : tmp) S[13][i] = 1;
  for (int i = 14; i <= n; i++) {
    C[i] = C[i - 2] + C[i - 1];
    for (int len = 1; len < s.size(); len++)
      if (S[i - 2][len] && P[i - 1][s.size() - len]) C[i]++;
    C[i] = min(C[i], k);
    for (int len = 0; len <= s.size(); len++) P[i][len] = P[i - 2][len];
    for (int len = 0; len <= s.size(); len++) S[i][len] = S[i - 1][len];
  }
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0);
  F[0] = "0";
  F[1] = "1";
  for (int i = 2; i < 14; i++) F[i] = F[i - 2] + F[i - 1];
  cin >> n >> k >> m;
  if (n < 14) {
    string ans = "", t0, t1;
    int c0, c1, cs0, cs1, len = 0;
    while (len < m) {
      len++;
      t0 = ans + '0';
      t1 = ans + '1';
      c0 = count(n, t0);
      c1 = count(n, t1);
      bool found;
      found = true;
      for (int i = 0; i < len; i++)
        if (t0[i] != F[n][F[n].size() - len + i]) found = false;
      cs0 = (found ? 1 : 0);
      found = true;
      for (int i = 0; i < len; i++)
        if (t1[i] != F[n][F[n].size() - len + i]) found = false;
      cs1 = (found ? 1 : 0);
      if (k <= cs0) {
        cout << (t0) << '\n', cin.ignore();
        cin.get();
        return 0;
      } else {
        k -= cs0;
        if (k <= c0)
          ans = t0;
        else {
          k -= c0;
          if (k <= cs1) {
            cout << (t1) << '\n', cin.ignore();
            cin.get();
            return 0;
          } else {
            k -= cs1;
            ans = t1;
          }
        }
      }
    }
    cout << (ans) << '\n', cin.ignore();
    cin.get();
    return 0;
  }
  string ans = "", t0, t1;
  long long c0, c1, cs0, cs1, len = 0;
  while (len < m) {
    len++;
    t0 = ans + '0';
    t1 = ans + '1';
    calc(t0);
    c0 = C[n];
    cs0 = S[n][len];
    calc(t1);
    c1 = C[n];
    cs1 = S[n][len];
    if (k <= cs0) {
      cout << (t0) << '\n', cin.ignore();
      cin.get();
      return 0;
    } else {
      k -= cs0;
      if (k <= c0)
        ans = t0;
      else {
        k -= c0;
        if (k <= cs1) {
          cout << (t1) << '\n', cin.ignore();
          cin.get();
          return 0;
        } else {
          k -= cs1;
          ans = t1;
        }
      }
    }
  }
  cout << ans << '\n';
  cin.ignore();
  cin.get();
  return 0;
}

```