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 PYTHON):

Solution:
from __future__ import division;
from bisect import *;
import sys;
from math import *;
from fractions import *;
from itertools import *;
import io;
import re;

INF = 987654321987654321987654321;

def readint(delimiter=' ') :
    return map(int, raw_input().split(delimiter));

def readstr(delimiter=' ') :
    return raw_input().split(delimiter);

def readfloat(delimiter=' ') :
    return map(float, raw_input().split(delimiter));

def index(a, x):
    'Locate the leftmost value exactly equal to x'
    i = bisect_left(a, x)
    if i != len(a) and a[i] == x:
        return i
    raise ValueError

def find_lt(a, x):
    'Find rightmost value less than x'
    i = bisect_left(a, x)
    if i:
        return a[i-1]
    raise ValueError

def find_le(a, x):
    'Find rightmost value less than or equal to x'
    i = bisect_right(a, x)
    if i:
        return a[i-1]
    raise ValueError

def find_gt(a, x):
    'Find leftmost value greater than x'
    i = bisect_right(a, x)
    if i != len(a):
        return a[i]
    raise ValueError

def find_ge(a, x):
    'Find leftmost item greater than or equal to x'
    i = bisect_left(a, x)
    if i != len(a):
        return a[i]
    raise ValueError

def bin_search(a, x, left, right) :

    while left<=right :
        mid = (left + right)//2;

        if a[mid] == x :
            return mid;
        elif a[mid] < x :
            left = mid + 1;
        elif a[mid] > x :
            right = mid - 1;

        pass

    return -1;
    pass

def printf(format, *args):
    """Format args with the first argument as format string, and write.
    Return the last arg, or format itself if there are no args."""
    sys.stdout.write(str(format) % args)
    pass

if __name__ == '__main__':

    n, k, p = readint();
    a = readint();
    a_odd = [];
    a_even = [];
    for a_item in a :
        if a_item % 2 == 0 :
            a_even.append(a_item);
        else :
            a_odd.append(a_item);
            pass
        pass
    need_even = p;
    need_odd = k-p;

    if need_odd > len(a_odd) :
        print "NO";
    elif len(a_odd) % 2 != need_odd % 2 :
        print "NO";
    elif need_even > ((len(a_odd) - need_odd) / 2 + len(a_even)) :
        print "NO"
    else :
        print "YES";

        part = [[] for _ in xrange(k)];
        idx = 0;
        while (need_even > 0) :
            if  len(a_even) > 0 :
                part[idx].append(a_even.pop());
            else :
                part[idx].append(a_odd.pop());
                part[idx].append(a_odd.pop());
                pass
                
            idx+=1;
            need_even -= 1;
            pass

        while (need_odd > 0) :
            part[idx].append(a_odd.pop());
            idx+=1;
            need_odd -= 1;
            pass

        while (len(a_even) > 0) :
            part[idx-1].append(a_even.pop());

        while (len(a_odd) > 0) :
            part[idx-1].append(a_odd.pop());

        for ii in xrange(k) :
            print len(part[ii]), ' '.join(map(str, part[ii]));

        pass

    pass