Problem: Devu being a small kid, likes to play a lot, but he only likes to play with arrays. While playing he came up with an interesting question which he could not solve, can you please solve it for him?

Given an array consisting of distinct integers. Is it possible to partition the whole array into k disjoint non-empty parts such that p of the parts have even sum (each of them must have even sum) and remaining k - p have odd sum? (note that parts need not to be continuous).

If it is possible to partition the array, also give any possible way of valid partitioning.

Input

The first line will contain three space separated integers n, k, p (1 ≤ k ≤ n ≤ 105; 0 ≤ p ≤ k). The next line will contain n space-separated distinct integers representing the content of array a: a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

In the first line print "YES" (without the quotes) if it is possible to partition the array in the required way. Otherwise print "NO" (without the quotes).

If the required partition exists, print k lines after the first line. The ith of them should contain the content of the ith part. Print the content of the part in the line in the following way: firstly print the number of elements of the part, then print all the elements of the part in arbitrary order. There must be exactly p parts with even sum, each of the remaining k - p parts must have odd sum.

As there can be multiple partitions, you are allowed to print any valid partition.

Examples

Input

5 5 3
2 6 10 5 9


Output

YES
1 9
1 5
1 10
1 6
1 2


Input

5 5 3
7 14 2 9 5


Output

NO


Input

5 3 1
1 2 3 7 5


Output

YES
3 5 1 3
1 7
1 2

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.util.*;

public class C439 {

    static int even = 0, odd = 0;
    static ArrayList<Integer> evens = new ArrayList<>();
    static ArrayList<Integer> odds = new ArrayList<>();

    public static void main(String[] args) throws Exception {
        int first[] = IO.nextIntArray(3, " ");
        int n = first[1], k = first[2], p = first[3];
        even = 0;
        odd = 0;
        evens.clear();
        odds.clear();
        int second[] = IO.nextIntArray(n, " ");

        boolean doable = true;
        int moreEven = 0;

        ArrayList<ArrayList<Integer>> ans = new ArrayList<>();

        int lastEven = -1;
        if (even >= p) {
            moreEven = even - p;
            for (int i = 0; i < p; ++i) {
                ans.add(new ArrayList<Integer>());
                ans.get(i).add(evens.remove(evens.size() - 1));
            }
            if(p>0)
            for (int i = 0; i < moreEven; ++i) { 
                ans.get(p - 1).add(evens.remove(evens.size() - 1));
            }

        } else if (even < p) {
            for (int i = 0; i < even; ++i) {
                ans.add(new ArrayList<Integer>());
                ans.get(i).add(evens.remove(evens.size() - 1));
            }
            int required = p - even;
            if (odd >= 2 * required) {
                odd -= 2 * required;
                for (int i = 0; i < required; ++i) {
                    ans.add(new ArrayList<Integer>());
                    ans.get(ans.size() - 1).add(odds.remove(odds.size() - 1));
                    ans.get(ans.size() - 1).add(odds.remove(odds.size() - 1));
                }
            } else {
                doable = false;
            }
        }
        
        lastEven = p - 1;

        if (odd < (k - p)) {
            doable = false;
        } else if (odd >= (k - p)) {
            int oddStart = ans.size();
            for (int i = 0; i < (k - p); ++i) {
                ans.add(new ArrayList<Integer>());
                ans.get(ans.size() - 1).add(odds.remove(odds.size() - 1));
            }
            int remainingOdds = odd - (k - p); 
            if (remainingOdds % 2 == 1) {
                    doable = false;
            } else { 
                for (int i = 0; i < remainingOdds; ++i) {
                    ans.get(ans.size() - 1).add(odds.remove(odds.size() - 1));
                }
            } 
            if(evens.size()>0){
                for(int a:evens)
                ans.get(ans.size()-1).add(a);
            }
        }

        if (!doable) {
            IO.println("NO");
        } else {
            IO.println("YES");
            for (ArrayList<Integer> al : ans) {
                IO.print(al.size() + " ");
                for (int i : al) {
                    IO.print(i + " ");
                }
                IO.println();
            }
        }
    }

    static class IO {

        static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public static int[][] next2dInt(int rows, int cols, String seperator) throws Exception {
            int[][] arr = new int[rows + 1][cols + 1];
            for (int i = 1; i <= rows; ++i) {
                arr[i] = nextIntArray(cols, seperator);
            }
            return arr;
        }

        public static int[] nextIntArray(int nInts, String seperator) throws IOException {
            String ints = br.readLine();
            String[] sArray = ints.split(seperator); 
            int[] array = new int[nInts + 1];
            for (int i = 1; i <= nInts; ++i) {
                array[i] = Integer.parseInt(sArray[i - 1]);
                if (array[i] % 2 == 0) {
                    even++; 
                    evens.add(array[i]);
                } else {
                    odd++;
                    odds.add(array[i]);
                }
            } 
            return array;
        }

        public static long[] nextLongArray(int nLongs, String seperator) throws IOException {
            String longs = br.readLine();
            String[] sArray = longs.split(seperator);
            long[] array = new long[nLongs + 1];
            for (int i = 1; i <= nLongs; ++i) {
                array[i] = Long.parseLong(sArray[i - 1]);
            }
            return array;
        }

        public static double[] nextDoubleArray(int nDoubles, String seperator) throws IOException {
            String doubles = br.readLine();
            String[] sArray = doubles.split(seperator);
            double[] array = new double[nDoubles + 1];
            for (int i = 1; i <= nDoubles; ++i) {
                array[i] = Double.parseDouble(sArray[i - 1]);
            }
            return array;
        }

        public static char[] nextCharArray(int nChars, String seperator) throws IOException {
            String chars = br.readLine();
            String[] sArray = chars.split(seperator);
            char[] array = new char[nChars + 1];
            for (int i = 1; i <= nChars; ++i) {
                array[i] = sArray[i - 1].charAt(0);
            }
            return array;
        }

        public static int nextInt() throws IOException {
            String in = br.readLine();
            return Integer.parseInt(in);
        }

        public static double nextDouble() throws IOException {
            String in = br.readLine();
            return Double.parseDouble(in);
        }

        public static long nextLong() throws IOException {
            String in = br.readLine();
            return Long.parseLong(in);
        }

        public static int nextChar() throws IOException {
            String in = br.readLine();
            return in.charAt(0);
        }

        public static String nextString() throws IOException {
            return br.readLine();
        }

        public static void print(Object... o) {
            for (Object os : o) {
                System.out.print(os);
            }
        }

        public static void println(Object... o) {
            for (Object os : o) {
                System.out.print(os);
            }
            System.out.print("\n");
        }

        public static void printlnSeperate(String seperator, Object... o) {
            StringBuilder sb = new StringBuilder();
            sb.delete(sb.length() - seperator.length(), sb.length());
            System.out.println(sb);
        }
    }
}