Tomorrow Ann takes the hardest exam of programming where she should get an excellent mark. 

On the last theoretical class the teacher introduced the notion of a half-palindrome. 

String t is a half-palindrome, if for all the odd positions i (<image>) the following condition is held: ti = t|t| - i + 1, where |t| is the length of string t if positions are indexed from 1. For example, strings "abaa", "a", "bb", "abbbaa" are half-palindromes and strings "ab", "bba" and "aaabaa" are not.

Ann knows that on the exam she will get string s, consisting only of letters a and b, and number k. To get an excellent mark she has to find the k-th in the lexicographical order string among all substrings of s that are half-palyndromes. Note that each substring in this order is considered as many times as many times it occurs in s.

The teachers guarantees that the given number k doesn't exceed the number of substrings of the given string that are half-palindromes.

Can you cope with this problem?

Input

The first line of the input contains string s (1 ≤ |s| ≤ 5000), consisting only of characters 'a' and 'b', where |s| is the length of string s.

The second line contains a positive integer k — the lexicographical number of the requested string among all the half-palindrome substrings of the given string s. The strings are numbered starting from one. 

It is guaranteed that number k doesn't exceed the number of substrings of the given string that are half-palindromes.

Output

Print a substring of the given string that is the k-th in the lexicographical order of all substrings of the given string that are half-palindromes.

Examples

Input

abbabaab
7


Output

abaa


Input

aaaaa
10


Output

aaa


Input

bbaabb
13


Output

bbaabb

Note

By definition, string a = a1a2... an is lexicographically less than string b = b1b2... bm, if either a is a prefix of b and doesn't coincide with b, or there exists such i, that a1 = b1, a2 = b2, ... ai - 1 = bi - 1, ai < bi.

In the first sample half-palindrome substrings are the following strings — a, a, a, a, aa, aba, abaa, abba, abbabaa, b, b, b, b, baab, bab, bb, bbab, bbabaab (the list is given in the lexicographical order). 
import java.util.*;

public class E2 {

//    private static class Node {
//        private final char symbol;
//        private int count;
//        private int totalCount;
//        private Node left;
//        private Node right;
//
//        public Node(char symbol) {
//            this.symbol = symbol;
//            this.count = 0;
//        }
//
//        public char getSymbol() {
//            return symbol;
//        }
//
//        public int getCount() {
//            return count;
//        }
//
//        public int getTotalCount() {
//            return totalCount;
//        }
//
//        public Node getLeft() {
//            return left;
//        }
//
//        public Node getRight() {
//            return right;
//        }
//
//        public void inc() {
//            ++count;
//        }
//
//        public void incTotal(int amount) {
//            totalCount += amount;
//        }
//
//        public void setLeft(Node node) {
//            this.left = node;
//        }
//
//        public void setRight(Node node) {
//            this.right = node;
//        }
//    }

    private static class Trie {
        int[] count;
        int[] left;
        int[] right;
        int index = 1;

        public Trie(String source) {
            int len = source.length() * source.length() + 2;
            count = new int[len];
            left = new int[len];
            right = new int[len];
        }

        public void add(String source, int start, int[] polyCount) {
            int len = source.length();
            int current = 1;
            count[current] += polyCount[start];
            for (int i = start; i < len; ++i) {
                if (source.charAt(i) == 'a') {
                    if (left[current] == 0) {
                        left[current] = ++index;
                    }
                    current = left[current];
                } else {
                    if (right[current] == 0) {
                        right[current] = ++index;
                    }
                    current = right[current];
                }
                count[current] += polyCount[i];
            }
        }

        public String search(int order) {
            int current = 1;
            StringBuilder builder = new StringBuilder();
            while (count[current] >= order) {
                order -= count[current] - count[left[current]] - count[right[current]];
                if (order <= 0) {
                    break;
                }
                if (order <= count[left[current]]) {
                    current = left[current];
                    builder.append('a');
                } else {
                    order -= count[left[current]];
                    current = right[current];
                    builder.append('b');
                }
            }
            return builder.toString();
        }

        @Override
        public String toString() {
            return "r " + Arrays.toString(right) +
                    "\nl " + Arrays.toString(left) +
                    "\nc " + Arrays.toString(count);
        }
    }

    private static String getHalfPolyndrome(String input, int order) {
        Trie trie = new Trie(input);
        int len = input.length();
        int polyCount[][] = new int[len][len];
        for (int i = 0; i < len; i++) {
            fillPolyndromes(input, i, i, polyCount);
            fillPolyndromes(input, i, i + 1, polyCount);
            fillPolyndromes(input, i, i + 2, polyCount);
            fillPolyndromes(input, i, i + 3, polyCount);
        }
        for (int i = 0; i < len; ++i) {
            for (int j = len - 2; j >= i; --j) {
                polyCount[i][j] += polyCount[i][j + 1];
            }
        }
        for (int i = 0; i < len; ++i) {
            trie.add(input, i, polyCount[i]);
        }
        return trie.search(order);
    }

    private static void fillPolyndromes(String input, int left, int right, int[][] polyCount) {
        while (left >= 0 && right < input.length() && input.charAt(left) == input.charAt(right)) {
            polyCount[left][right] = 1;
            left -= 2;
            right += 2;
        }
    }

    private static List<String> getHalfPolyndromesBrute(String input) {
        List<String> halfPolyndromes = new ArrayList<>();
        for (int i = 0; i < input.length(); ++i) {
            fillPolyndromesBrute(input, i, i, halfPolyndromes);
            fillPolyndromesBrute(input, i, i + 1, halfPolyndromes);
            fillPolyndromesBrute(input, i, i + 2, halfPolyndromes);
            fillPolyndromesBrute(input, i, i + 3, halfPolyndromes);
        }
        Collections.sort(halfPolyndromes);
        return halfPolyndromes;
    }

    private static void fillPolyndromesBrute(String input, int left, int right, List<String> collector) {
        while (left >= 0 && right < input.length() && input.charAt(left) == input.charAt(right)) {
            collector.add(input.substring(left, right + 1));
            left -= 2;
            right += 2;
        }
    }

    private static String generateInput(Random r, int length, double skew) {
        StringBuilder builder = new StringBuilder(length);
        for (int i = 0; i < length; i++) {
            builder.append(r.nextDouble() > skew ? 'a' : 'b');
        }
        return builder.toString();
    }

    private static void solve() {
        Scanner s = new Scanner(System.in);
        String input = s.next();
        int k = s.nextInt();
        String result = getHalfPolyndrome(input, k);
        System.out.println(result);
    }

    private static void test() {
        Random r = new Random(137);
        for (int i = 0; i < 100; ++i) {
            int length = r.nextInt(100);
            String input = generateInput(r, length, 0.5);
            List<String> result = getHalfPolyndromesBrute(input);
            for (int j = 0; j < result.size(); ++j) {
                String expected = result.get(j);
                String actual = getHalfPolyndrome(input, j + 1);
                if (!expected.equals(actual)) {
                    System.out.println("TEST FAILURE");
                    System.out.println("INPUT    : " + j + " " + input);
                    System.out.println("EXPECTED : " + expected);
                    System.out.println("GOT      : " + actual);
                    getHalfPolyndrome(input, j + 1);
                    System.exit(1);
                }
            }
        }
        System.out.println("LOGIC TEST PASSED");

        for (int i = 0; i < 100; ++i) {
            long start = System.currentTimeMillis();
            r = new Random(137);
            String input = generateInput(r, 5000, 0.5);
            getHalfPolyndrome(input, 100);
            long elapsed = System.currentTimeMillis() - start;
            if (elapsed > 5000) {
                System.out.println(input);
            }
            System.out.println("Elapsed " + String.valueOf(elapsed) + " ms");
        }
    }

    public static void main(String[] args) {
        solve();
    }
}
