A new Berland businessman Vitaly is going to open a household appliances' store. All he's got to do now is to hire the staff.

The store will work seven days a week, but not around the clock. Every day at least k people must work in the store.

Berland has a law that determines the order of working days and non-working days. Namely, each employee must work for exactly n consecutive days, then rest for exactly m days, then work for n more days and rest for m more, and so on. Vitaly doesn't want to break the law. Fortunately, there is a loophole: the law comes into force on the day when the employee is hired. For example, if an employee is hired on day x, then he should work on days [x, x + 1, ..., x + n - 1], [x + m + n, x + m + n + 1, ..., x + m + 2n - 1], and so on. Day x can be chosen arbitrarily by Vitaly.

There is one more thing: the key to the store. Berland law prohibits making copies of keys, so there is only one key. Vitaly is planning to entrust the key to the store employees. At the same time on each day the key must be with an employee who works that day — otherwise on this day no one can get inside the store. During the day the key holder can give the key to another employee, if he also works that day. The key will handed to the first hired employee at his first working day.

Each employee has to be paid salary. Therefore, Vitaly wants to hire as few employees as possible provided that the store can operate normally on each day from 1 to infinity. In other words, on each day with index from 1 to infinity, the store must have at least k working employees, and one of the working employees should have the key to the store.

Help Vitaly and determine the minimum required number of employees, as well as days on which they should be hired.

Input

The first line contains three integers n, m and k (1 ≤ m ≤ n ≤ 1000, n ≠ 1, 1 ≤ k ≤ 1000).

Output

In the first line print a single integer z — the minimum required number of employees.

In the second line print z positive integers, separated by spaces: the i-th integer ai (1 ≤ ai ≤ 104) should represent the number of the day, on which Vitaly should hire the i-th employee.

If there are multiple answers, print any of them.

Examples

Input

4 3 2


Output

4
1 1 4 5

Input

3 3 1


Output

3
1 3 5

import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.Vector;

/**
 * 4 4
 * 1 5 3 4
 * 1 2
 * 1 3
 * 2 3
 * 3 3
 *
 *
 * @author pttrung
 */
public class A {

    public static long Mod = (long) (1e9) + 7;
    static int[][] dp;
    static int[] X = {0, -1, 0, 1};
    static int[] Y = {-1, 0, 1, 0};

    public static void main(String[] args) throws FileNotFoundException {
        PrintWriter out = new PrintWriter(System.out);
        //PrintWriter out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        Scanner in = new Scanner();
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        int last = n + m;
        int cur = n - 1;


        ArrayList<Integer> list = new ArrayList();
        for (int i = 0; i < k; i++) {
            list.add(1);
        }
        boolean first = true;
        while (cur < last) {
            
            
            if (cur + 2 < last || first) {
                list.add(cur + 1);
                for (int i = 0; i < k - 1; i++) {
                    list.add(cur + 2);
                }
            }else{
                if(cur + 2 == last && k > 1){
                    list.add(cur + 2);
                }else{
                    list.add(cur + 1);
                }
            }
            first = false;
            cur += n - 1;
            if (cur + 1>= last && k > 1) {
                break;
            }
           // out.println(cur);
        }
        out.println(list.size());
        for (int i : list) {
            out.print(i + " ");
        }

        out.close();
    }

    static long[] extendEuclid(long a, long b) {
        if (b == 0) {
            return new long[]{a, 1, 0};
        }
        long[] re = extendEuclid(b, a % b);
        long x = re[2];
        long y = re[1] - (a / b) * re[2];
        re[1] = x;
        re[2] = y;
        return re;

    }

    static long[] modularLinearSolver(long a, long b, long n) {
        long[] ex = extendEuclid(a, n);
        if (b % ex[0] != 0) {
            throw new IllegalArgumentException("No solution");
        }
        long[] result = new long[(int) n];
        result[0] = (ex[1] * (b / ex[0])) % n;
        for (int i = 1; i < n; i++) {
            result[i] = result[0] + i * (n / ex[0]);
        }
        return result;
    }

    static int[] KMP(String v) {
        int i = 0, j = -1;

        int[] result = new int[v.length() + 1];
        result[0] = -1;
        while (i < v.length()) {
            while (j >= 0 && v.charAt(i) != v.charAt(j)) {
                j = result[j];
            }
            i++;
            j++;
            result[i] = j;
        }
        return result;
    }

    static int find(int index, int[] u) {
        if (index != u[index]) {
            return u[index] = find(u[index], u);
        }
        return index;
    }

    public static long pow(int a, int b, long mod) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long v = pow(a, b / 2, mod);
        if (b % 2 == 0) {
            return (v * v) % mod;
        } else {
            return (((v * v) % mod) * a) % mod;
        }
    }

    public static int[][] powSquareMatrix(int[][] A, long p) {
        int[][] unit = new int[A.length][A.length];
        for (int i = 0; i < unit.length; i++) {
            unit[i][i] = 1;
        }
        if (p == 0) {
            return unit;
        }
        int[][] val = powSquareMatrix(A, p / 2);
        if (p % 2 == 0) {
            return mulMatrix(val, val);
        } else {
            return mulMatrix(A, mulMatrix(val, val));
        }

    }

    public static int[][] mulMatrix(int[][] A, int[][] B) {
        int[][] result = new int[A.length][B[0].length];
        for (int i = 0; i < result.length; i++) {
            for (int j = 0; j < result[0].length; j++) {
                long temp = 0;
                for (int k = 0; k < A[0].length; k++) {

                    temp += ((long) A[i][k] * B[k][j] % Mod);
                    temp %= Mod;
                }
                temp %= Mod;
                result[i][j] = (int) temp;
            }
        }

        return result;
    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;




    }

    static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        void update(int index, int val) {
            // System.out.println("UPDATE INDEX " + index);
            while (index < data.length) {
                data[index] += val;
                index += index & (-index);

                //    System.out.println("NEXT " +index);
            }
        }

        long get(int index) {
            //  System.out.println("GET INDEX " + index);
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= index & (-index);
                // System.out.println("BACK " + index);
            }
            return result;
        }

        public String toString() {
            return Arrays.toString(data);
        }
    }

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

    static long pow(long a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {

            return val * val % Mod;
        } else {
            return (val * val % Mod) * a % Mod;
        }
    }

//    static Point intersect(Point a, Point b, Point c) {
//        double D = cross(a, b);
//        if (D != 0) {
//            return new Point(cross(c, b) / D, cross(a, c) / D);
//        }
//        return null;
//    }
//
//    static Point convert(Point a, double angle) {
//        double x = a.x * cos(angle) - a.y * sin(angle);
//        double y = a.x * sin(angle) + a.y * cos(angle);
//        return new Point(x, y);
//    }
    static Point minus(Point a, Point b) {
        return new Point(a.x - b.x, a.y - b.y);
    }
//
//    static Point add(Point a, Point b) {
//        return new Point(a.x + b.x, a.y + b.y);
//    }
//

    /**
     * Cross product ab*ac
     *
     * @param a
     * @param b
     * @param c
     * @return
     */
    static double cross(Point a, Point b, Point c) {
        Point ab = new Point(b.x - a.x, b.y - a.y);
        Point ac = new Point(c.x - a.x, c.y - a.y);
        return cross(ab, ac);
    }

    static double cross(Point a, Point b) {
        return a.x * b.y - a.y * b.x;
    }

    /**
     * Dot product ab*ac;
     *
     * @param a
     * @param b
     * @param c
     * @return
     */
    static long dot(Point a, Point b, Point c) {
        Point ab = new Point(b.x - a.x, b.y - a.y);
        Point ac = new Point(c.x - a.x, c.y - a.y);
        return dot(ab, ac);
    }

    static long dot(Point a, Point b) {
        long total = a.x * b.x;
        total += a.y * b.y;
        return total;
    }

    static double dist(Point a, Point b) {
        long total = (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
        return Math.sqrt(total);
    }

    static long norm(Point a) {
        long result = a.x * a.x;
        result += a.y * a.y;
        return result;
    }

    static double dist(Point a, Point b, Point x, boolean isSegment) {
        double dist = cross(a, b, x) / dist(a, b);
        // System.out.println("DIST " + dist);

        if (isSegment) {
            Point ab = new Point(b.x - a.x, b.y - a.y);

            long dot1 = dot(a, b, x);
            long norm = norm(ab);
            double u = (double) dot1 / norm;
            if (u < 0) {
                return dist(a, x);
            }

            if (u > 1) {
                return dist(b, x);
            }
        }
        return Math.abs(dist);




    }

    static long squareDist(Point a, Point b) {
        long x = a.x - b.x;
        long y = a.y - b.y;
        return x * x + y * y;
    }

    static class Point {

        int x, y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Point{" + "x=" + x + ", y=" + y + '}';
        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            //System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //br = new BufferedReader(new FileReader(new File("input.txt")));
        }

        public String next() {


            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}
