Problem: Given are three integers N, K, and S.

Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.

* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.

Constraints

* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K S


Output

Print a sequence satisfying the condition, in the following format:


A_1 A_2 ... A_N

Output

Print a sequence satisfying the condition, in the following format:


A_1 A_2 ... A_N

Examples

Input

4 2 3


Output

1 2 3 4


Input

5 3 100


Output

50 50 50 30 70

Solution (in JAVA):

Solution:

import java.util.*;
import java.io.*;
class Main {
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        int k = sc.nextInt();
        int s = sc.nextInt();
        long[] a = new long[n];
        if(k==0) {
            long damy = (long)1e9;
            if(s==(long)1e9) damy = (long)1e9-2;
            for(int i = 0; i<n; i++) {
                a[i] = damy;
                pp(a[i]+" ");
            }
            p("");
            return;
        }
        if(s==1) {
            long damy = (long)1e9;
            if(s==(long)1e9) damy = (long)1e9-2;
            for(int i = 0; i<n; i++) {
                if(i<k)a[i] = 1;
                else a[i] = 2;
                pp(a[i]+" ");
            }
            p("");
            return;
        }
        if(k==1) {
            long damy = (long)1e9;
            if(s==(long)1e9) damy = (long)1e9-2;
            for(int i = 0; i<n; i++) {
                if(i==0) a[i] = s;
                else a[i] = damy;
                pp(a[i]+" ");
            }
            p("");
            return;
        }
        // long damy = (long)1e9;
        // if(s==(long)1e9) damy = (long)1e9-2;

        // for(int i = 0; i<n; i++) {
        //     if(i%2==0) a[i] = 1;
        //     else a[i] = s-1;
        //     if(i>k) a[i] = damy;
        //     pp(a[i]+" ");
        // }

        // p("");
        // return;
        long damy = (long)1e9;
        if(s==(long)1e9) damy = (long)1e9-2;
        for(int i = 0; i<n; i++) {
            if(i<k)a[i] = s;
            else a[i] = damy;
            pp(a[i]+" ");
        }
        p("");
        return;

        // if(k%2!=0) {
        //     long damy = (long)1e9;
        //     if(s==(long)1e9) damy = (long)1e9-1;

        //     for(int i = 0; i<n; i++) {
        //         if(i%=0) a[i] = 1;
        //         else a[i] = s-1;
        //         if(i>=k) a[i] = damy;
        //         p(a[i]);
        //     }
        //     return;
        // }

    }
    public static <T> void p(T element) {
	    System.out.println(element);
    }
    public static <T> void pp(T element) {
	    System.out.print(element);
    }
    public static <T> void pe(T element) {
        System.err.println(element);
    }
    public static int min(int a, int b, int c) {
	int min = Math.min(a,b);
	min = Math.min(min,c);
	return min;
    }
    public static int max(int a, int b,int c) {
	int max= Math.max(a,b);
	max = Math.max(max,c);
        return max;
    }
}
class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
 
    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }
 
    private boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }
 
    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }
 
    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
 
    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
 
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }
 
    public double nextDouble() {
        return Double.parseDouble(next());
    }
}