Problem: Olya likes milk very much. She drinks k cartons of milk each day if she has at least k and drinks all of them if she doesn't. But there's an issue — expiration dates. Each carton has a date after which you can't drink it (you still can drink it exactly at the date written on the carton). Due to this, if Olya's fridge contains a carton past its expiry date, she throws it away.

Olya hates throwing out cartons, so when she drinks a carton, she chooses the one which expires the fastest. It's easy to understand that this strategy minimizes the amount of cartons thrown out and lets her avoid it if it's even possible.

<image> Milk. Best before: 20.02.2017.

The main issue Olya has is the one of buying new cartons. Currently, there are n cartons of milk in Olya's fridge, for each one an expiration date is known (how soon does it expire, measured in days). In the shop that Olya visited there are m cartons, and the expiration date is known for each of those cartons as well.

Find the maximum number of cartons Olya can buy so that she wouldn't have to throw away any cartons. Assume that Olya drank no cartons today. 

Input

In the first line there are three integers n, m, k (1 ≤ n, m ≤ 106, 1 ≤ k ≤ n + m) — the amount of cartons in Olya's fridge, the amount of cartons in the shop and the number of cartons Olya drinks each day.

In the second line there are n integers f1, f2, ..., fn (0 ≤ fi ≤ 107) — expiration dates of the cartons in Olya's fridge. The expiration date is expressed by the number of days the drinking of this carton can be delayed. For example, a 0 expiration date means it must be drunk today, 1 — no later than tomorrow, etc.

In the third line there are m integers s1, s2, ..., sm (0 ≤ si ≤ 107) — expiration dates of the cartons in the shop in a similar format.

Output

If there's no way for Olya to drink the cartons she already has in her fridge, print -1.

Otherwise, in the first line print the maximum number x of cartons which Olya can buy so that she wouldn't have to throw a carton away. The next line should contain exactly x integers — the numbers of the cartons that should be bought (cartons are numbered in an order in which they are written in the input, starting with 1). Numbers should not repeat, but can be in arbitrary order. If there are multiple correct answers, print any of them.

Examples

Input

3 6 2
1 0 1
2 0 2 0 0 2


Output

3
1 2 3

Input

3 1 2
0 0 0
1


Output

-1

Input

2 1 2
0 1
0


Output

1
1 

Note

In the first example k = 2 and Olya has three cartons with expiry dates 0, 1 and 1 (they expire today, tomorrow and tomorrow), and the shop has 3 cartons with expiry date 0 and 3 cartons with expiry date 2. Olya can buy three cartons, for example, one with the expiry date 0 and two with expiry date 2.

In the second example all three cartons Olya owns expire today and it means she would have to throw packets away regardless of whether she buys an extra one or not.

In the third example Olya would drink k = 2 cartons today (one she alreay has in her fridge and one from the shop) and the remaining one tomorrow.

Solution (in JAVA):

Solution:
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class SuffixArray {
	private static InputStream stream;
	private static byte[] buf = new byte[1024];
	private static int curChar;
	private static int numChars;
	private static SpaceCharFilter filter;
	private static PrintWriter pw;
	private static long max = Long.MIN_VALUE;
	private static int mod = 1000000000 + 7;

	private static void soln() {
		int n=nextInt();
		int m=nextInt();
		int k=nextInt();
		int[] arr=nextIntArray(n);
		Arrays.sort(arr);
		long[] arr1=new long[m];
		for(long i=0;i<m;i++){
			arr1[(int) i]=nextLong()<<32 | i;
		}
		Arrays.sort(arr1);
		int[] dd=new int[10000003];
		int l=10000005;
		for(int i=n-1;i>=0;i--){
			l=Math.min(l,arr[i]);
			if(l<0){
				System.out.println(-1);
				System.exit(0);
			}
			dd[l]++;
			if(dd[l]==k)
				l--;
		}
		l=0;
		int[] ans=new int[m];
		int tot=0;
		for(int i=0;i<m;i++){
			while(dd[l]==k) l++;
			if(l<=arr1[i]>>>32){
				ans[tot++]=(int)arr1[i]+1;
				dd[l]++;
			}
		}
		pw.println(tot);
		for(int i=0;i<tot;i++)
			pw.print(ans[i]+" ");
	}
	static long y;
	private static long po(long a,long b){
		if(b==0){
			y=0;
			return 1;
		}
		long tmp=po(b,a%b);
		long x=y;
		y=tmp-(a/b)*y;
		return x;
	}
	private static void traverse(LinkedList<Integer>[] l,int cur,int prev,long[][][] dp){
		if(l[cur].size()==1 && prev!=-1){
			dp[cur][0][0]=1;
			dp[cur][1][0]=1;
		}else{
			dp[cur][0][0]=1;
			dp[cur][0][1]=1;
			dp[cur][1][0]=1;
			dp[cur][1][1]=1;
			Iterator<Integer> i=l[cur].listIterator();
			while(i.hasNext()){
				int x=i.next();
				if(x!=prev){
					traverse(l,x,cur,dp);
					dp[cur][0][0]=(dp[cur][0][0]*(dp[x][1][1]))%mod;
					dp[cur][0][1]=(dp[cur][0][1]*(dp[x][1][1]+dp[x][0][0]+dp[x][0][1]))%mod;
					dp[cur][1][0]=(dp[cur][1][0]*(dp[x][0][1]))%mod;
					dp[cur][1][1]=(dp[cur][1][1]*(dp[x][0][1]+dp[x][1][0]+dp[x][1][1]))%mod;
				}
			}
			dp[cur][0][1]=(dp[cur][0][1]-dp[cur][0][0]+mod)%mod;
			dp[cur][1][1]=(dp[cur][1][1]-dp[cur][1][0]+mod)%mod;
		}
		//System.out.println((cur+1)+" "+dp[cur][0][0]+" "+dp[cur][0][1]+" "+dp[cur][1][0]+" "+dp[cur][1][1]);
	}
	private static boolean check1(int a,int b,int n,boolean[][] v){
		if(a==0 && a<n && b>=0 && b<n && !v[a][b])
			return true;
		return false;
	}
	public static class Suffix implements Comparable<Suffix>{
		int index;
		int[] rank=new int[2];
		@Override
		public int compareTo(Suffix arg0){
			return (this.rank[0]==arg0.rank[0])?(this.rank[1]<arg0.rank[1]?-1:1):(this.rank[0]<arg0.rank[0]?-1:1);
		}	
	}
	private static int[] buildSuffix(String s,int n){
		Suffix[] arr=new Suffix[n];
		for(int i=0;i<n;i++)
			arr[i]=new Suffix();
		for(int i=0;i<n;i++){
			arr[i].index=i;
			arr[i].rank[0]=s.charAt(i)-'a';
			arr[i].rank[1]=((i+1)<n)?(s.charAt(i+1)-'a'):-1;
		}
		Arrays.sort(arr);
		//for(int i=0;i<n;i++)
			//System.out.print(arr[i].index);
		int[] ind=new int[n];
		for(int k=4;k<2*n;k=k*2){
			int rank=0;
			int p_rank=arr[0].rank[0];
			arr[0].rank[0]=rank;
			ind[arr[0].index]=0;
			for(int i=1;i<n;i++){
				if (arr[i].rank[0] == p_rank && arr[i].rank[1] == arr[i-1].rank[1]) {
	                p_rank = arr[i].rank[0];
	                arr[i].rank[0] = rank;
	            }
	            else{
	                p_rank = arr[i].rank[0];
	                arr[i].rank[0] = ++rank;
	            }
	            ind[arr[i].index] = i;
	        }
			for(int i=0;i<n;i++){
				int n_index=arr[i].index + k/2;
				arr[i].rank[1]=(n_index<n)?arr[ind[n_index]].rank[0] : -1;
			}
			Arrays.sort(arr);
		}
		int[] suffixArr=new int[n];
		for(int i=0;i<n;i++)
			suffixArr[i]=arr[i].index;
		return suffixArr;
	}
	private static long pow(long a, long b, long c) {
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}
	
	private static class Pair implements Comparable<Pair> {
		long x;
		int y;

		public Pair(long a, int x2) {
			x = a;
			y = x2;
		}

		@Override
		public int compareTo(Pair arg0) {
			return (int) (this.x-arg0.x);
		}
	}

	private static long gcd(long a, long res1) {
		if (res1 == 0)
			return a;
		return gcd(res1, a % res1);
	}

	private static long max(long a, long b) {
		if (a > b)
			return a;
		return b;
	}

	private static long min(long a, long b) {
		if (a < b)
			return a;
		return b;
	}

	public static void main(String[] args) throws Exception {
		InputReader(System.in);
		pw = new PrintWriter(System.out);
		soln();
		pw.close();
	}

	public static void InputReader(InputStream stream1) {
		stream = stream1;
	}

	private static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private static boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}

	private static int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	private static int nextInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private static long nextLong() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private static String nextToken() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private static String nextLine() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}

	private static int[] nextIntArray(int n) {
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextInt();
		}
		return arr;
	}

	private static long[] nextLongArray(int n) {
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextLong();
		}
		return arr;
	}

	private static void pArray(int[] arr) {
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private static void pArray(long[] arr) {
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private static boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	private interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}