permutation sequence

class Solution {
public:
  string getPermutation(int n, int k) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        if( k <= 0 ) return "";
        
        vector<int> flag(n, 0 );
        for( int i=0;i<n;i++ )  flag[i] = i+1;
        int N = 1;
        
        for(int i=n;i>=1;i--)
            N *= i;
        if( k > N )  k = k % N;
      
        N /= n;
        string s = "";
        int t;
        while(  k > 0 )
        {
            t = ceil( (float)k / N ) - 1 ;
            s += (char)('0' + flag[t] );
            flag.erase( flag.begin() + t, flag.begin() + t + 1 );
            if( flag.empty() )    return s;
            k = k - t* N;  
            N /= flag.size();
        }

        
        return s;
    }
};