Permutations

You are given a permutation p of numbers 1, 2, …, n. Let’s define f(p) as the following sum:

Find the lexicographically m-th permutation of length n in the set of permutations having the maximum possible value of f(p).

Input

The single line of input contains two integers n and m (1 ≤ m ≤ cnt _n), where cnt _n is the number of permutations of length n with maximum possible value of f(p).

The problem consists of two subproblems. The subproblems have different constraints on the input. You will get some score for the correct submission of the subproblem. The description of the subproblems follows.

• In subproblem B1 (3 points), the constraint 1 ≤ n ≤ 8 will hold.
• In subproblem B2 (4 points), the constraint 1 ≤ n ≤ 50 will hold.

Output

Output n number forming the required permutation.Examplesinput

2 2

output

2 1 

input

3 2

output

1 3 2 

Note

In the first example, both permutations of numbers {1, 2} yield maximum possible f(p) which is equal to 4. Among them, (2, 1) comes second in lexicographical order.

Solution:

#include <cstring>
#include <vector>
#include  	<list>
#include

<map>
#include <set>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <memory.h>
#include <cassert>

using namespace std;

int ans[777];

int main() {
int n;
long long m;
cin >> n >> m;
int l = 0, r = n - 1;
for (int j = n - 1; j > 0; j--) {
if (m <= (1LL << (j - 1))) {
      ans[l++] = n - j;
    } else {
      ans[r--] = n - j;
      m -= (1LL << (j - 1));
    }
  }
  ans[l] = n;
  for (int i = 0; i < n; i++) cout << ans[i] << " ";
  cout << endl;
  return 0;
}