Problem: Vasya the Great Magician and Conjurer loves all kinds of miracles and wizardry. In one wave of a magic wand he can turn an object into something else. But, as you all know, there is no better magic in the Universe than the magic of numbers. That's why Vasya adores math and spends a lot of time turning some numbers into some other ones.

This morning he has n cards with integers lined up in front of him. Each integer is not less than 1, but not greater than l. When Vasya waves his magic wand, two rightmost cards vanish from the line and a new card magically appears in their place. It contains the difference between the left and the right numbers on the two vanished cards. Vasya was very interested to know what would happen next, and so he waved with his magic wand on and on, until the table had a single card left.

Suppose that Vasya originally had the following cards: 4, 1, 1, 3 (listed from left to right). Then after the first wave the line would be: 4, 1, -2, and after the second one: 4, 3, and after the third one the table would have a single card with number 1.

Please note that in spite of the fact that initially all the numbers on the cards were not less than 1 and not greater than l, the numbers on the appearing cards can be anything, no restrictions are imposed on them.

It is now evening. Vasya is very tired and wants to return everything back, but does not remember which cards he had in the morning. He only remembers that there were n cards, they contained integers from 1 to l, and after all magical actions he was left with a single card containing number d.

Help Vasya to recover the initial set of cards with numbers.

Input

The single line contains three space-separated integers: n (2 ≤ n ≤ 100) — the initial number of cards on the table, d (|d| ≤ 104) — the number on the card that was left on the table after all the magical actions, and l (1 ≤ l ≤ 100) — the limits for the initial integers.

Output

If Vasya is mistaken, that is, if there doesn't exist a set that meets the requirements given in the statement, then print a single number -1, otherwise print the sought set containing n integers from 1 to l. Separate the integers by spaces. Print the integers in the order, in which they were written on the cards from left to right. If there are several suitable sets of numbers, you can print any of them.

Examples

Input

3 3 2


Output

2 1 2 

Input

5 -4 3


Output

-1


Input

5 -4 4


Output

2 4 1 4 1 

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class CF1 implements Runnable {

    static FastReader sc;
    static PrintWriter out;
    static int mod = 1000000007, inf = (int) 1e9, minf = -(int) 1e9;
    static long infL = (long) 1e18, minfL = -(long) 1e18;

    public static void main(String[] args) {
        new Thread(null, new CF1(), "coderrohan14", 1 << 26).start();
    }

    @Override
    public void run() {
        try {
            ioSetup();
        } catch (IOException e) {
            return;
        }
    }

    public static void ioSetup() throws IOException {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            File f1 = new File("input.txt");
            File f2 = new File("output.txt");
            Reader r = new FileReader(f1);
            sc = new FastReader(r);
            out = new PrintWriter(f2);
            double prev = System.currentTimeMillis();
            solve();
            out.println("\n\nExecuted in : " + ((System.currentTimeMillis() - prev) / 1e3) + " sec");
        } else {
            sc = new FastReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            solve();
        }
        out.flush();
        out.close();
    }

    static int n, d, l, dp[][];
    static ArrayList<Integer> arr;

    static void solve() {
        // int t = sc.nextInt();
        // StringBuilder ans = new StringBuilder("");
        // while (t-- > 0) {

        // }
        // out.println(ans);
        n = sc.nextInt();
        d = sc.nextInt();
        l = sc.nextInt();
        arr = new ArrayList<>();
        dp = new int[n + 1][30000];
        for (int i = 0; i <= n; i++) {
            for (int j = 0; j < 30000; j++) {
                dp[i][j] = minf;
            }
        }
        if (helper(1, 0)) {
            Collections.reverse(arr);
            for (Integer e : arr) {
                out.print(e + " ");
            }
        } else {
            out.println(-1);
        }
    }

    static boolean helper(int i, int sum) {
        if (i == n + 1) {
            // if (sum == d)
            // out.println(sum + " " + d);
            return sum == d;
        }
        if (sum >= 0) {
            if (dp[i][sum] != minf)
                return dp[i][sum] == 1;
        } else {
            if (dp[i][10000 - sum] != minf) {
                return dp[i][10000 - sum] == 1;
            }
        }
        boolean z = false;
        int s = (i % 2 == 0) ? -1 : 1;
        for (int x = 1; x <= l; x++) {
            if (helper(i + 1, (s * x) + sum)) {
                // out.println(sum);
                arr.add(x);
                z = true;
                break;
            }
        }
        if (z) {
            if (sum >= 0) {
                dp[i][sum] = 1;
            } else {
                dp[i][10000 - sum] = 1;
            }
        } else {
            if (sum >= 0) {
                dp[i][sum] = 2;
            } else {
                dp[i][10000 - sum] = 2;
            }
        }
        return z;
    }

    /****************************************************************************************************************************************************************************************/

    public static int log2(int N) {
        int result = (int) (Math.log(N) / Math.log(2));
        return result;
    }

    static int countSetBits(long n) {
        int count = 0;
        while (n > 0) {
            n &= (n - 1);
            count++;
        }
        return count;
    }

    static long modInverse(long a, int mod) {
        long g = gcd(a, mod);
        if (g != 1)
            return -1;
        else {
            return modPower(a, mod - 2L, mod);
        }
    }

    static long modPower(long x, long y, int mod) {
        long res = 1;
        x = x % mod;
        if (x == 0)
            return 0;
        while (y > 0) {
            if ((y & 1) != 0)
                res = (res * x) % mod;
            y = y >> 1;
            x = (x * x) % mod;
        }
        return res;
    }

    static int gcd(int a, int b) {
        int tmp = 0;
        while (b != 0) {
            tmp = b;
            b = a % b;
            a = tmp;
        }
        return a;
    }

    static long gcd(long a, long b) {
        long tmp = 0;
        while (b != 0) {
            tmp = b;
            b = a % b;
            a = tmp;
        }
        return a;
    }

    static boolean isPrime(long n) {
        if (n == 2 || n == 3)
            return true;
        if (n % 2 == 0)
            return false;
        for (long i = 3; i * i <= n; i += 2) {
            if (n % i == 0)
                return false;
        }
        return n != 1;
    }

    static boolean isPerfectSquare(long x) {
        long sqrt = (long) Math.sqrt(x);
        return (sqrt * sqrt) == x;
    }

    static int digitsCount(long x) {
        return (int) Math.floor(Math.log10(x)) + 1;
    }

    static boolean isPowerTwo(long n) {
        return (n & n - 1) == 0;
    }

    static void sieve(boolean[] prime, int n) { // Sieve Of Eratosthenes
        for (int i = 1; i <= n; i++) {
            prime[i] = true;
        }
        for (int i = 2; i * i <= n; i++) {
            if (prime[i]) {
                for (int j = 2; i * j <= n; j++) {
                    prime[i * j] = false;
                }
            }
        }
    }

    static long nCr(long n, long r) { // Combinations
        if (n < r)
            return 0;
        if (r > n - r) { // because nCr(n, r) == nCr(n, n - r)
            r = n - r;
        }
        long ans = 1L;
        for (long i = 0; i < r; i++) {
            ans *= (n - i);
            ans /= (i + 1);
        }
        return ans;
    }

    static int floor(int[] a, int v) {
        int l = 0, h = a.length - 1;
        while (l < h) {
            int mid = (l + h) / 2;
            if (a[mid] == v)
                return mid;
            if (v < a[mid])
                h = mid;
            else {
                if (mid + 1 < h && a[mid + 1] < v)
                    l = mid + 1;
                else
                    return mid;
            }
        }
        return a[l] <= v ? l : -1;
    }

    static int floor(long[] a, long v) {
        int l = 0, h = a.length - 1;
        while (l < h) {
            int mid = (l + h) / 2;
            if (a[mid] == v)
                return mid;
            if (v < a[mid])
                h = mid;
            else {
                if (mid + 1 < h && a[mid + 1] < v)
                    l = mid + 1;
                else
                    return mid;
            }
        }
        return a[l] <= v ? l : -1;
    }

    static int ceil(int[] a, int v) {
        int l = 0, h = a.length - 1;
        while (l < h) {
            int mid = (l + h) / 2;
            if (a[mid] == v)
                return mid;
            if (a[mid] < v)
                l = mid + 1;
            else
                h = mid;
        }
        return a[h] >= v ? h : -1;
    }

    static int ceil(long[] a, long v) {
        int l = 0, h = a.length - 1;
        while (l < h) {
            int mid = (l + h) / 2;
            if (a[mid] == v)
                return mid;
            if (a[mid] < v)
                l = mid + 1;
            else
                h = mid;
        }
        return a[h] >= v ? h : -1;
    }

    static long catalan(int n) { // n-th Catalan Number
        long c = nCr(2 * n, n);
        return c / (n + 1);
    }

    static class Pair implements Comparable<Pair> { // Pair Class
        long x;
        long y;

        public Pair(long x, long y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (!(o instanceof Pair)) {
                return false;
            }

            Pair pair = (Pair) o;

            if (x != pair.x) {
                return false;
            }
            if (y != pair.y) {
                return false;
            }

            return true;
        }

        @Override
        public int hashCode() {
            long result = x;
            result = 31 * result + y;
            return (int) result;
        }

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

    static class Trip { // Triplet Class
        long x;
        long y;
        long z;

        Trip(long x, long y, long z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (!(o instanceof Trip)) {
                return false;
            }

            Trip trip = (Trip) o;

            if (x != trip.x) {
                return false;
            }
            if (y != trip.y) {
                return false;
            }
            if (z != trip.z) {
                return false;
            }
            return true;
        }

        @Override
        public int hashCode() {
            long result = 62 * x + 31 * y + z;
            return (int) result;
        }
    }

    /**************************************************************************************************************************************************************************************/

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader(Reader r) {
            br = new BufferedReader(r);
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        int[] readArrayI(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = sc.nextInt();
            }
            return arr;
        }

        long[] readArrayL(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = sc.nextLong();
            }
            return arr;
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        boolean hasNext() {
            if (st != null && st.hasMoreTokens()) {
                return true;
            }
            String tmp;
            try {
                br.mark(1000);
                tmp = br.readLine();
                if (tmp == null) {
                    return false;
                }
                br.reset();
            } catch (IOException e) {
                return false;
            }
            return true;
        }
    }

    /*
     * ASCII Range--->(A-Z)--->[65,90]<<::>>(a-z)--->[97,122]
     */
    /******************************************************************************************************************/

    static void printArray(int[] arr) {
        out.print("[");
        for (int i = 0; i < arr.length; i++) {
            if (i < arr.length - 1)
                out.print(arr[i] + ",");
            else
                out.print(arr[i]);
        }
        out.print("]");
        out.println();
    }

    static void printArray(long[] arr) {
        out.print("[");
        for (int i = 0; i < arr.length; i++) {
            if (i < arr.length - 1)
                out.print(arr[i] + ",");
            else
                out.print(arr[i]);
        }
        out.print("]");
        out.println();
    }

    static void printArray(double[] arr) {
        out.print("[");
        for (int i = 0; i < arr.length; i++) {
            if (i < arr.length - 1)
                out.print(arr[i] + ",");
            else
                out.print(arr[i]);
        }
        out.print("]");
        out.println();
    }
    /**********************************************************************************************************************/
}