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.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;

/**
 * Created by Firеfly on 1/1/2017.
 */
public class Task {
    public static void main(String[] args) throws IOException {
        Emaxx emaxx = new Emaxx();
    }
}


class Emaxx {
    static char[] checker;
    FScanner fs;
    PrintWriter pw;
    long MOD = 1000000007;
    HashMap<Integer, Integer> map[];
    int[] mmas;
    int n, m;
    long[][] desk;
    long sum;
    boolean used[];
    ArrayList<Integer> graph[];
    HashMap<Integer, Integer>[] answer;
    int max;
    int[] hi;
    int[] sums;
    int par;
    int[] parent;
    int[] temp;
    Emaxx() throws IOException {
        fs = new FScanner(new InputStreamReader(System.in));
        // pw = new PrintWriter(new FileWriter("arithnumbers.out"));
        //  fs = new FScanner(new FileReader("C:\\Users\\Firеfly\\Desktop\\New Text Document.txt"));
        //     fs = new FScanner(new FileReader("input.txt"));;
        //       pw = new PrintWriter("output.txt");
        pw = new PrintWriter(System.out);
        int n = fs.nextInt();
        int m = fs.nextInt();
        int k = fs.nextInt();
        int[] mas = new int[n];
        int[][] mas1 = new int[m][2];
        for (int i = 0; i<n; i++)
            mas[i] = fs.nextInt();
        for (int i = 0; i<m; i++) {
            mas1[i][0] = fs.nextInt();
            mas1[i][1] = i + 1;
        }
        Arrays.sort(mas);
        boolean able = true;
        int day = 0;
        for (int i = 0; i<n; i++) {
            for (int p = i;p<n && p<i+k; p++)
            {
                if (mas[p]<day)
                    able = false;
            }
            day++;
            i +=k-1;
        }
        if (!able)
        {
            System.out.println(-1);
            System.exit(0);
        }
        Arrays.sort(mas1, new Comparator<int[]>() {
            @Override
            public int compare(int[] o1, int[] o2) {
                return -Integer.compare(o1[0], o2[0]);
            }
        });
        int min = 0;
        int max = m;
        while (min!=max) {
            int med = (max+1+min)/2;
            able = true;
            day = 0;
            for (int i = 0, j = med-1; i<n || j>=0;) {
                for (int p = 0; p<k; p++) {
                    if (i>=n && j<0)
                        break;
                    else if (i>=n) {
                        if (mas1[j][0]<day)
                            able = false;
                        j--;
                    } else if (j<0) {
                        if (mas[i]<day)
                            able = false;
                        i++;
                    } else if (mas[i]<mas1[j][0]){
                        if (mas[i]<day)
                            able = false;
                        i++;
                        } else {
                            if (mas1[j][0]<day)
                                able = false;
                            j--;
                    }
                }
                day++;
            }
            if (!able) {
                max = med-1;
            } else min = med;
        }
        pw.println(max);
        for (int i = 0; i<max; i++)
            pw.print(mas1[i][1] + " ");
        pw.close();
    }

    int dfs_for_root(int v) {
        for (int i = 0; i<graph[v].size(); i++)
        {
            if (sums[graph[v].get(i)] == sum/3)
                return graph[v].get(i);
            int p = dfs_for_root(graph[v].get(i));
            if (p !=-1)
                return p;
        }
        return -1;
    }
    int make(int[][] orig, int[] combs) {
        for (int i = 3; i<10; i++) {
            for (int j = 0; j<3; j++) {
                int curp = 0;
                int f = 0;
                int s = 1;
                int th = 2;
                if (combs[0] == 1)
                    f+=j;
                if (combs[2] == 1)
                    s+=j;
                if (combs[4] == 1)
                    th+=j;
                int f1 = 0;
                int s1 = 0;
                int th1 = 0;
                if (combs[1] == 1)
                    f1 = i-3;
                if (combs[3] == 1)
                    s1 = i-3;
                if (combs[5] == 1)
                    th1 = i-3;
                orig[i][j] = orig[f1][f] + orig[s1][s] + orig[th1][th];
            }
        }
        return orig[9][2];
    }
    int inv(Pair mas[]) {
        int ans = 0;
        for (int i = 1; i<n; i++) {
            System.out.println(mas[i].x + " " + mas[i].y);
            for (int j = i-1; j>=0; j--) {
                if (mas[j].y>mas[i].y)
                    ans++;
            }
        }
        return ans;
    }


    double len(double x1, double x2, double y1, double y2) {
        return Math.sqrt((x2-x1)*(x2-x1)+(y1-y2)*(y1-y2));
    }

    int find(int cub, int prev) {
        if (cub == 0)
            return 1;
        int ans = 0;
        for (int i = prev+1; i<=cub; i++) {
            ans+=find(cub-i, i);
        }
        return ans;
    }
    int findNum(char[] mas) {
        int size = 1;
        int i  =0 , j = 0;
        for (i = 1,j = mas.length-1; i<=j; i++, j--)
            if ((mas[i]>='0' && mas[i]<='9') || (mas[j]>='0' && mas[j] <='9'))
                break;
            else size++;
        if (i>j)
            return -1;
        else
            return size;
    }

    int findsymb(char[] mas) {
        int size = 1;
        int i = 0, j = 0;
        for (i = 1,j = mas.length-1; i<=j; i++, j--)
            if ((mas[i]>='a' && mas[i]<='z') || (mas[j]>='a' && mas[j] <='z'))
                break;
            else size++;
        if (i>j)return -1;
        else
            return size;
    }

    int findlitts(char[] mas) {
        int size = 1;
        int i= 0, j = 0;
        for (i = 1,j = mas.length-1; i<=j; i++, j--)
            if (mas[i]=='&' || mas[i]=='*' || mas[i] == '#' || mas[j]=='*' || mas[j] =='#' || mas[j] == '&')
                break;
            else size++;
        if (i>j)
            return -1;
        else
            return size;
    }

    boolean ans(int[] second, int first[], int start) {
        int fir = 0;
        int sec = start;
        while (sec<n && first[0] != second[sec])
            sec++;
        int p = sec;
        if (sec == n) {
            return false;}
        else {
            while (sec<n && first[fir] == second[sec])
            {
                sec++;
                fir++;
            }
            if (sec!=n) {
                return false;
            }
            else {
                sec = 0;
                while (sec < p && second[sec] == first[fir]) {
                    sec++;
                    fir++;
                }
                if (sec != p)
                    return false;
                else
                    return true;
            }
        }
    }

    int dfs(int v) {
        used[v] = true;
        sums[v] = temp[v];
        for (int i = 0; i<graph[v].size(); i++) {
            if (!used[graph[v].get(i)]) {
                sums[v]+= dfs(graph[v].get(i));
            }
        }
        return sums[v];
    }



    int gcd (int a, int b) {
        if (b == 0)
            return a;
        else
            return gcd(b, a % b);
    }



    /*

        int l1 = le[le.length-1]-46;
        int l2 = le[le.length-2]-46;
        if (l1>=l2)
            l1-=l2;
        else l1 = l1+10-l2;
        System.out.println(l1);
        long ll = dp[le.length][l1];
        int r1 = re[re.length-1]-46;
        int r2 = re[re.length-2]-46;
        if (r1>=r2)
            r1 -=r2;
        else r1 = r1+10-r2;
        long rr = dp[re.length][r1];
     */
    void PP(int[] mas) {
        System.out.println("WAT");
        ArrayList<Character> list = new ArrayList<>();
        for (int i = 0; i<mas.length; i++) {
            System.out.println(mas[i]);
            while (mas[i] > 0) {
                list.add((char) (i + 48));
                mas[i]--;
            }
        }
        Collections.sort(list);
        for (int i = list.size()-1; i>=0; i--)
            pw.print(list.get(i));
    }

    boolean good(int i, int j) {
        if ((i>=0) && (i<n) && (j>=0) && (j<m))
            return true;
        else return false;
    }

    long solve(int i, int j) {
        if (good(i, j))
        {
            if (desk[i][j]==0)
                desk[i][j] += solve(i-1, j-2)+solve(i-2, j-1)+solve(i+1, j-2)+solve(i-2, j+1);
        } else return 0;
        return desk[i][j];
    }
    boolean check(char c) {
        for (int i = 0;i<checker.length; i++)
            if (c == checker[i])
                return true;
        return false;
    }
    void make_set (int v) {
        parent[v] = v;
    }

    int find_set (int v) {
        if (v == parent[v])
            return v;
        return find_set (parent[v]);
    }

    void union_sets (int a, int b) {
        a = find_set (a);
        b = find_set (b);
        if (a != b)
            parent[b] = a;
    }

    static class IntegerUtils {
        public static long[] generateFactorials(int limit, long MOD) {
            long[] result = new long[limit];
            result[0] = 1;
            if (limit == 0) return result;
            for (int i = 1; i < limit; ++i) {
                result[i] = (result[i - 1] * i) % MOD;
            }
            return result;
        }
    }

    int[] Z_function(char[] arr) { //начинается как в начале и идёт как в начале
        int n = arr.length;
        int[] z = new int[n];
        z[0] = 0;
        for (int i = 1, l = 0, r = 0; i<n; i++) {
            if (i<=r)
                z[i] = Math.min(r-i+1, z[i-l]);
            while (i+z[i]<n && arr[i+z[i]] == arr[z[i]])
                z[i]++;
            if (i+z[i]-1>r)
            {
                l = i;
                r = i+z[i]-1;
            }
        }
        return z;
    }

    int[] prefix_function(char[] arr) { // оканчивается на этот символ
        int n = arr.length;
        int[] z = new int[n];
        for (int i = 1; i<n; i++) {
            int j = z[i-1];
            while (j>0 && arr[i] != arr[j]) {
                j=z[j-1];
            }
            if (arr[i] == arr[j]) j++;
            z[i] = j;
        }
        return z;
    }

    long substrings_string(char[] arr) {
        int p = 31;
        int n = arr.length;
        long[] pows = new long[n];
        pows[0] = 1;
        for (int i = 1; i<n; i++)
            pows[i] = pows[i-1]*p;
        long[] prefixes = new long[n];
        for (int i = 0; i<n; i++) {
            prefixes[i] = (arr[i]-'a'+1)*pows[i];
            if (i!=0) prefixes[i]+=prefixes[i-1];
        }

        long res = 0;
        for (int l = 1; l<=n; l++) {
            HashSet<Long> hh = new HashSet<>();
            for (int i = 0; i<n-l+1; i++) {
                long cur_hash = prefixes[i+l-1];
                if (i!=0) cur_hash-=prefixes[i-1];
                cur_hash *= pows[n-i-1];
                hh.add(cur_hash);
            }
            res+=hh.size();
        }
        return res;
    }

    void rabin_Karp(char[] t, char[] s) {
        int p = 31;
        long[] p_pow = new long[Math.max(t.length, s.length)];
        p_pow[0] = 1;
        for (int i = 1; i<p_pow.length; i++)
            p_pow[i] = p_pow[i-1]*p;
        long main_hash = 0;
        for (int i = 0; i<s.length; i++)
            main_hash+=(s[i]-'a'+1)*p_pow[i];
        long hashes[] = new long[t.length];
        for (int i = 0; i<t.length; i++) {
            hashes[i] = (t[i]-'a'+1)*p_pow[i];
            if (i!=0) hashes[i]+=hashes[i-1];
        }
        for (int i = 0; i+s.length-1<t.length; i++) {
            long cur_h = hashes[i+s.length-1];
            if (i!=0) cur_h-=hashes[i-1];
            if (cur_h*p_pow[i] == main_hash)
                System.out.println(i);
        }
    }

    int[] podpalindroms(ArrayList<Character> s) {
        int n = s.size();
        int[] d1 = new int[n]; //odd
        int l = 0;
        int r = -1;
        for(int i = 0; i < n; i++) {
            int k;
            if (i > r) k = 1;
            else k = Math.min(d1[l + r - i], r - i);

            while (0 <= i - k && i + k < n && s.get(i - k) == s.get(i + k)) k++;
            d1[i] = k;
            if (i + k - 1 > r) {
                r = i + k - 1;
                l = i - k + 1;
            }
        }
        int[] res = new int[n];
        for (int i = 0; i<n; i++) {
            System.out.print(d1[i] + " ");
            res[i] = d1[i];
        }
        System.out.println();
        return res;
    }



}

class FScanner {
    BufferedReader br;
    StringTokenizer st;
    FScanner(InputStreamReader isr) {
        br = new BufferedReader(isr);
    }

    FScanner(FileReader fr) {
        br = new BufferedReader(fr);
    }

    String nextToken() throws IOException{
        while (st == null || !st.hasMoreTokens()) {
            String s = br.readLine();
            if (s == null)
                return null;
            st = new StringTokenizer(s);
        }
        return st.nextToken();
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    String nextLine() throws IOException {
        return br.readLine();
    }

    char nextChar() throws IOException {
        return (char) br.read();
    }

}

class Gangsta  {
    int t, s, p;
    void setT(int t1) {
        t = t1;
    }
    void setS(int s1) {
        s = s1;
    }
    void setP(int p1) {
        p = p1;
    }


}

class Pair implements Comparable<Pair> {
    int y, x;
    Pair(int x1, int y1) {
        x = x1;
        y = y1;
    }
    @Override
    public int compareTo(Pair o) {
        return -Integer.compare(x, o.x);
    }
}