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.BufferedWriter;
	import java.io.IOException;
	import java.io.OutputStreamWriter;
	import java.io.ObjectInputStream.GetField;
	import java.math.BigInteger;
	import java.util.ArrayList;
	import java.util.Arrays;
	import java.util.Collections;
	import java.util.HashMap;
	import java.util.HashSet;
	import java.util.InputMismatchException;
	import java.util.LinkedList;
	import java.util.List;
	import java.util.Map;
	import java.util.PriorityQueue;
	import java.util.Queue;
	import java.util.Stack;
	import java.util.TreeMap;
	import java.util.TreeSet;
	public class Q2 {
		
		static long MOD = 1000000007;
		static boolean b1,b[],bc[];
		static boolean boo[][][];
		static int ans1 = -1,ans2 = -1, root;
		static ArrayList<Integer>[] amp,amp1;
		static int sum[],dist[],cnt[];
		static long ans = 0;
		static long p = 0;
		//static ArrayList<Pair3>[][][] pmp;
		static FasterScanner sc = new FasterScanner();
		static Queue<Integer> q = new LinkedList<>();
		static int arr[],start[],end[],color[];
		static PriorityQueue<Integer> pq;
		//static ArrayList<Integer> parent = new ArrayList<>();
		static LinkedList<Integer> fa;
		static BufferedWriter log;
		static TreeMap<Integer,Integer> tm = new TreeMap<>();
		static HashSet<Integer> hs = new HashSet<>();
		static Stack<Integer> stack = new Stack<>();
		static Pair prr[];
		static long parent1[],parent2[],size[][],size1[],size2[],value[];
		public static void main(String[] args) throws Exception {
	    	new Thread(null, new Runnable() {
				public void run() {
					try {
						soln();
					} catch (Exception e) {
						e.printStackTrace();
					}
				}
			}, "1", 1 << 27).start();
	    }
		static int MAX = 10000001;
		public static void soln() throws IOException {
			log = new BufferedWriter(new OutputStreamWriter(System.out));
			int n = sc.nextInt(), m = sc.nextInt(), k = sc.nextInt();
			int f1[] = new int[MAX];
			int f2[] = new int[MAX];
			int sum[] = new int[MAX];
			int sum2[] = new int[MAX];
			for(int i = 0; i<n;i++){
				f1[sc.nextInt()]++;
			}
			int cnt = 0, sum1 = 0;
			long cnt1 = 0;
			for(int i =0 ; i< MAX;i++){
				sum1+=f1[i];
				cnt1+=k;
				if(sum1>cnt1){
					System.out.println(-1);
					return;
				}
				sum[i] = sum1;
			}
			for(int i = MAX-1;i>=0;i--){
				if(i<(MAX-1))
				sum2[i] = (int) Math.min(sum2[i+1],1L*(i+1)*k-sum[i]);
				else sum2[i] = (int) Math.min(MAX,1L*(i+1)*k-sum[i]);
			}
			cnt = 1;
			HashMap<Integer,ArrayList<Integer>> hm = new HashMap<>();
			for(int i = 0; i<m;i++){
				int x = sc.nextInt();
				if(hm.containsKey(x)){
					hm.get(x).add(cnt++);
				}
				else{
					ArrayList<Integer> a = new ArrayList<>();
					a.add(cnt++);
					hm.put(x, a);
				}
				f2[x]++;
			}
			ArrayList<Integer> arr = new ArrayList<>();
			for(int i =0 ;i<MAX;i++){
				long h = Math.min(f2[i],sum2[i]-ans);
					ans+=h;
					if(hm.containsKey(i)){
					ArrayList<Integer> temp = hm.get(i);
					for(int j =0 ;j< h;j++){
						//log.write(temp.get(j)+" ");
						arr.add(temp.get(j));
					}
				}
			}
			log.write(ans+"\n");
			for(int i:arr) log.write(i+" ");
			log.close();
		}
		public static int dfs(int x) throws IOException{
			if(b1) return 0;
			int ans = arr[x];
			b[x] = true;
			for(int e:amp[x]){
				if(b1) return 0;
				if(!b[e]){
					ans+=dfs(e);
				}
			}
		//	System.out.println(value[x]+" "+p);
			if(x!=root && ans==p){
				if(ans1==-1){
					ans1 = x+1;
					ans = 0;
				}
				else if(ans2==-1){
					ans2 = x+1;
					ans = 0;
					System.out.println(ans1+" "+ans2);
					System.exit(0);
				}
			}
			if(b1) return 0;
			return ans;
		}
		static boolean check(long arr1[] , long arr2[] , int key ,int x){
			for(int i =0 ; i< key && i<arr1.length ;i++){
				long sum = 0;
				if((key-(i+1))<=arr2.length){
					if((key-(i+1))!=0)
					sum += (arr1[i]+arr2[key-(i+1)-1]);
					else sum = arr1[i];
					if(sum<=x) return true;
				}
			}
			if(key>0 && key<=arr2.length && arr2[key-1]<=x) return true;
			return false;
		}
		public static int binarySearch(long arr[],long key){
			int low = 0, high = arr.length-1;
			while(low<high){
				int mid = (high+low+1)/2;
				if(arr[mid] >= key) low = mid;
				else high = mid-1;
			}
			if(arr[low]<key)
			return low+1;
			else return 0;
		}
		public static void bfs(int x,int arr[]){
		b = new boolean[arr.length];
		b[x] = true;
		q = new LinkedList<>();
		q.add(x);
		while(!q.isEmpty()){
			int y = q.poll();
			for(int i = 0;i<amp[y].size();i++) {
				if(!b[amp[y].get(i)]){
					q.add(amp[y].get(i));
					b[amp[y].get(i)] = true;
					arr[amp[y].get(i)] = (arr[y]+1);
				}
			}
		}
		}
		
		static long get(long x){
			if((x%10)<5) return x-(x%10);
			else return x+(10-x%10);
		}
		
		static long func(long n, long d, long t){
			return (t*(2*(n-1)+(t-1)*(d)))/2;
		}
		static class Pair implements Comparable<Pair> {
			int u;
			int v;
			public Pair(int u, int v) {
				this.u = u;
				this.v = v;
			}
			
			public int hashCode() {
				int hu = (int) (u ^ (u >>> 32));
				int hv = (int) (v ^ (v >>> 32));
				return 31*hu + hv;
			}
	 
			public boolean equals(Object o) {
				Pair other = (Pair) o;
				return (u == other.u && v == other.v);
			}
	 
			public int compareTo(Pair other) {
				return Integer.compare(u, other.u) != 0 ? (Integer.compare(u, other.u)) : (Integer.compare(v, other.v));
			}
			
			public String toString() {
				return "[u=" + u + ", v=" + v + "]";
			}
		}
		public static void buildGraph(int n){
			for(int i =0;i<n;i++){
				int x = sc.nextInt(), y = sc.nextInt();
				amp[--x].add(--y);
				amp[y].add(x);
			}
		}
		
		
		public static long getParent(long x, long parent[]){
			while(parent[(int) x]!=x){
				parent[(int) x] = parent[(int) parent[(int) x]];
				x = parent[(int) x];
			}
			return x;
		}
		static long min(long a, long b, long c){
			if(a<b && a<c) return a;
			if(b<c) return b;
			return c;
		}
		/*
		static void dfs3D(int x,int y,int z){
			ans++;
			boo[x][y][z] = true;
			for(Pair3 e:pmp[x][y][z]){
				if(!boo[e.x][e.y][e.z]){
					dfs3D(e.x,e.y,e.z);
				}
			}
		}
		static class Pair3{
			int x, y ,z;
			Pair3(int x, int y, int z){
				this.x = x;
				this.y = y;
				this.z = z;
			}
		}*/
		static int sum(int n){
			String str = Integer.toString(n);
			int cnt = 0;
			for(int i = 0; i< str.length();i++){
				cnt+=(str.charAt(i)-'0');
			}
			return cnt;
		}
		 static void KMPSearch(String pat, String txt)
		    {
		        int M = pat.length();
		        int N = txt.length();
		 
		        // create lps[] that will hold the longest
		        // prefix suffix values for pattern
		        int lps[] = new int[M];
		        int j = 0;  // index for pat[]
		 
		        // Preprocess the pattern (calculate lps[]
		        // array)
		        computeLPSArray(pat,M,lps);
		 
		        int i = 0;  // index for txt[]
		        while (i < N)
		        {
		            if (pat.charAt(j) == txt.charAt(i))
		            {
		                j++;
		                i++;
		            }
		            if (j == M)
		            {
		               // parent.add((i-j));
		                j = lps[j-1];
		            }
		 
		            // mismatch after j matches
		            else if (i < N && pat.charAt(j) != txt.charAt(i))
		            {
		                // Do not match lps[0..lps[j-1]] characters,
		                // they will match anyway
		                if (j != 0)
		                    j = lps[j-1];
		                else
		                    i = i+1;
		            }
		        }
		    }
		 static void computeLPSArray(String pat, int M, int lps[])
		    {
		        // length of the previous longest prefix suffix
		        int len = 0;
		        int i = 1;
		        lps[0] = 0;  // lps[0] is always 0
		 
		        // the loop calculates lps[i] for i = 1 to M-1
		        while (i < M)
		        {
		            if (pat.charAt(i) == pat.charAt(len))
		            {
		                len++;
		                lps[i] = len;
		                i++;
		            }
		            else  // (pat[i] != pat[len])
		            {
		                // This is tricky. Consider the example.
		                // AAACAAAA and i = 7. The idea is similar 
		                // to search step.
		                if (len != 0)
		                {
		                    len = lps[len-1];
		 
		                    // Also, note that we do not increment
		                    // i here
		                }
		                else  // if (len == 0)
		                {
		                    lps[i] = len;
		                    i++;
		                }
		            }
		        }
		    }
		private static void permutation(String prefix, String str) {
		    int n = str.length();
		    if (n == 0); //hs.add(prefix);
		    else {
		        for (int i = 0; i < n; i++)
		            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
		    }
		}
		public static char give(char c1,char c2){
			if(c1!='a' && c2!='a') return 'a';
			if(c1!='b' && c2!='b') return 'b';
			return 'c';
		}
		static class Graph{
			int vertex;
			long weight;
		}
		public static void buildTree(int n){
			int arr[] = sc.nextIntArray(n);
			for(int i = 0;i<n;i++){
				int x = arr[i]-1;
				amp[i+1].add(x);
				amp[x].add(i+1);
			}
		}
		
		
		static class SegmentTree{
			int pre[], suf[], max[], val[];
			SegmentTree( int n){
				int size = 4*n;
				pre = new int[size];
				suf = new int[size];
				max = new int[size];
				val = new int[size];
				build(0,n-1,1);
			}
			void build(int ss, int se, int si){
				if(ss==se){
					pre[si] = 1;
					suf[si] = 1;
					max[si] = 1;
					val[si] = arr[ss];
				}
				else{
				int mid = (ss+se)>>2;
				si*=2;
				build(ss,mid,si);build(mid+1,se,si+1);
				}
			}
			
			/*int[] get(int qs, int qe, int ss, int se, int si){
				if(qe < ss || se < qs)
	        		return new int[2];
				if(qs<=ss && qe>=se){
					return new int[]{max[si],val[si]};
				}
				int mid = (ss+se)/2;
				si*=2;
				if(qe<=mid) return get(qs,qe,ss,mid,si);
				else if(qs>mid) return get(qs,qe,mid+1,se,si+1);
				long a1[] = build(ss,mid,si*2), a2[] = build(mid+1,se,si*2+1);
				long ans[] = new long[4];
				if(arr[mid] == arr[mid+1]){
				    long temp = a1[2]+a2[0];
				    if(temp>=a2[1] && temp>=a1[1]){
				        ans[1] = temp;
				        ans[3] = arr[mid];
				    }
				    else if(a2[1]>=a1[1]){
				        ans[1] = a2[1];
				        ans[3] = a2[3];
				    }
				    else{
				        ans[1] = a1[1];
				        ans[3] = a1[3];
				    } 
				    if(a1[1]==(mid-ss+1)) ans[0] = ans[1];
				    else ans[0] = a1[0];
				    if(a2[2]==(se-mid)) ans[2] = ans[1];
					else ans[2] = a2[2];
				}
				else{
					if(a2[1]>=a1[1]){
				        ans[1] = a2[1];
				        ans[3] = a2[3];
				    }
				    else{
				        ans[1] = a1[1];
				        ans[3] = a1[3];
				    } 
					ans[0] = a1[0];
					ans[2] = a2[2];
				}
	            return ans;
			}
			void print(){
				for(int i = 0;i<st.length;i++){
					System.out.println(st[i][0]+" "+st[i][1]+" "+st[i][2]+" "+st[i][3]);
				}
				System.out.println();
			}*/
		}
		static int convert(int x){
			int cnt = 0;
			String str = Integer.toBinaryString(x);
			//System.out.println(str);
			for(int i = 0;i<str.length();i++){
				if(str.charAt(i)=='1'){
					cnt++;
				}
			}
			int ans = (int) Math.pow(3, 6-cnt);
			return ans;
		}
		static class Node2{
			Node2 left = null;
			Node2 right = null;
			Node2 parent = null;
			int data;
		}
		static class BinarySearchTree{
			Node2 root = null;
			int height = 0;
			int max = 0;
			int cnt = 1;
			ArrayList<Integer> parent = new ArrayList<>();
			HashMap<Integer, Integer> hm = new HashMap<>();
			public void insert(int x){
				Node2 n = new Node2();
				n.data = x;
				if(root==null){
					root = n;
				}
				else{
					Node2 temp = root,temp2 = null;
					while(temp!=null){
						temp2 = temp;
						if(x>temp.data) temp = temp.right;
						else temp = temp.left;
					}
					if(x>temp2.data) temp2.right = n;
					else temp2.left = n;
					n.parent = temp2;
					parent.add(temp2.data);
				}
			}
			public Node2 getSomething(int x, int y, Node2 n){
				if(n.data==x || n.data==y) return n;
				else if(n.data>x && n.data<y) return n;
				else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
				else return getSomething(x,y,n.left);
			}
			public Node2 search(int x,Node2 n){
				if(x==n.data){
					max = Math.max(max, n.data);
					return n;
				}
				if(x>n.data){
					max = Math.max(max, n.data);
					return search(x,n.right);
				}
				else{
					max = Math.max(max, n.data);
					return search(x,n.left);
				}
			}
			public int getHeight(Node2 n){
				if(n==null) return 0;
				height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
				return height;
			}
		}
		static long findDiff(long[] arr, long[] brr, int m){
			int i = 0, j = 0;
			long fa = 1000000000000L;
			while(i<m && j<m){
				long x = arr[i]-brr[j];
				if(x>=0){
					if(x<fa) fa = x;
					j++;
				}
				else{
					if((-x)<fa) fa = -x;
					i++;
				}
			}
			return fa;
		}
		public static long max(long x, long y, long z){
			if(x>=y && x>=z) return x;
			if(y>=x && y>=z) return y;
			return z;
		}
		
		public static void seive(long n){
			b = new boolean[(int) (n+1)];
			Arrays.fill(b, true);
			for(int i = 2;i*i<=n;i++){
				if(b[i]){
					for(int p = 2*i;p<=n;p+=i){
						b[p] = false;
					}
				}
			}
		}
		static long modInverse(long a, long mOD2){
		            return  power(a, mOD2-2, mOD2);
		}
		static long power(long x, long y, long m)
		{
		    if (y == 0)
		        return 1;
		    long p = power(x, y/2, m) % m;
		    p = (p * p) % m;
		 
		    return (y%2 == 0)? p : (x * p) % m;
		}
		static long power2(long x,BigInteger y,long m){
			long ans = 1;
			BigInteger two = new BigInteger("2");
			while(y.compareTo(BigInteger.ZERO)>0){
				if(y.getLowestSetBit()==y.bitCount()){
					x = (x*x)%MOD;
					y = y.divide(two);
				}
				else{
					ans = (ans*x)%MOD;
					y = y.subtract(BigInteger.ONE);
				}
			}
			return ans;
		}
		static BigInteger power2(BigInteger x, BigInteger y, BigInteger m){
			BigInteger ans = new BigInteger("1");
			BigInteger one  = new BigInteger("1");
			BigInteger two  = new BigInteger("2");
			BigInteger zero  = new BigInteger("0");
			while(y.compareTo(zero)>0){
				//System.out.println(y);
				if(y.mod(two).equals(one)){
					ans = ans.multiply(x).mod(m);
					y = y.subtract(one);
				}
				else{
					x = x.multiply(x).mod(m);
					y = y.divide(two);
				}
			}
			return ans;
		}
		static BigInteger power(BigInteger x, BigInteger y, BigInteger m)
		{
		    if (y.equals(0))
		        return (new BigInteger("1"));
		    BigInteger p = power(x, y.divide(new BigInteger("2")), m).mod(m);
		    p = (p.multiply(p)).mod(m);
		 
		    return (y.mod(new BigInteger("2")).equals(0))? p : (p.multiply(x)).mod(m);
		}
		static long d,x,y;
		public static void extendedEuclidian(long a, long b){
			if(b == 0) {
		        d = a;
		        x = 1;
		        y = 0;
		    }
		    else {
		        extendedEuclidian(b, a%b);
		        int temp = (int) x;
		        x = y;
		        y = temp - (a/b)*y;
		    }
		}
		
		public static long gcd(long n, long m){
			if(m!=0) return gcd(m,n%m);
			else return n;
		}
		
		
		public static class FasterScanner {
			private byte[] buf = new byte[1024];
			private int curChar;
			private int numChars;
	 
			public int read() {
				if (numChars == -1)
					throw new InputMismatchException();
				if (curChar >= numChars) {
					curChar = 0;
					try {
						numChars = System.in.read(buf);
					} catch (IOException e) {
						throw new InputMismatchException();
					}
					if (numChars <= 0)
						return -1;
				}
				return buf[curChar++];
			}
	 
			public 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();
			}
	 
			public String nextString() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isSpaceChar(c));
				return res.toString();
			}
	 
			public 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;
			}
	 
			public 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;
			}
		        
		    public int[] nextIntArray(int n) {
		        return nextIntArray(n, 0);
		    }
		    
		    public int[] nextIntArray(int n, int off) {
		    	int[] arr = new int[n + off];
		    	for (int i = 0; i < n; i++) {
		    		arr[i + off] = nextInt();
		    	}
		    	return arr;
		    }
		    
		    public long[] nextLongArray(int n) {
		    	return nextLongArray(n, 0);
		    }
	        
			public long[] nextLongArray(int n, int off) {
			    long[] arr = new long[n + off];
			    for (int i = 0; i < n; i++) {
			        arr[i + off] = nextLong();
			    }
			    return arr;
			}
	 
		    private boolean isSpaceChar(int c) {
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
	 
			private boolean isEndOfLine(int c) {
				return c == '\n' || c == '\r' || c == -1;
			}
		}
	}