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public class Solution {
    public String getPermutation(int n, int k) {
        StringBuilder sb = new StringBuilder();
        boolean[] used = new boolean[n + 1];        
        int fac = 1;
        for (int i = 1; i <= n; i++)
            fac *= i;
        k--;
        for (int i = 0; i < n; i++){
            fac /= n - i;
            int idx = k / fac;
            for (int j = 1; j <= n; j++){
                if (used[j]) continue;
                if (idx == 0){
                    sb.append(j);
                    used[j] = true;
                    k = k % fac;
                    break;
                } else
                    idx--;
            }
        }
        
        return sb.toString();
    }
    
}

public class Solution {
public String getPermutation(int n, int k) {
    int pos = 0;
    List<Integer> numbers = new ArrayList<>();
    int[] factorial = new int[n+1];
    StringBuilder sb = new StringBuilder();
    
    // create an array of factorial lookup
    int sum = 1;
    factorial[0] = 1;
    for(int i=1; i<=n; i++){
        sum *= i;
        factorial[i] = sum;
    }
    // factorial[] = {1, 1, 2, 6, 24, ... n!}
    
    // create a list of numbers to get indices
    for(int i=1; i<=n; i++){
        numbers.add(i);
    }
    // numbers = {1, 2, 3, 4}
    
    k--;
    
    for(int i = 1; i <= n; i++){
        int index = k/factorial[n-i];
        sb.append(numbers.get(index));
        numbers.remove(index);
        k-=index*factorial[n-i];
    }
    
    return sb.toString();
}
}