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.io.IOException;
import java.io.InputStream;
import java.util.*;
import java.lang.*;


public class Main{
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int n = sc.nextInt();
		int k = sc.nextInt();
		int s = sc.nextInt();
		if (s != 1000000000) {
			if (n == k) {
				for (int i = 0; i < n - 1; i++) {
					System.out.print(s);
					System.out.print(" ");
				}
				System.out.println(s);
				return;
			}
			for (int i = 0; i < k; i++) {
				System.out.print(s);
				System.out.print(" ");
			}
			for (int i = 0; i < n - k - 1; i++) {
				System.out.print(1000000000);
				System.out.print(" ");
			}
			System.out.println(1000000000);

		} else {
			if (n == k) {
				for (int i = 0; i < n - 1; i++) {
					System.out.print(s);
					System.out.print(" ");
				}
				System.out.println(s);
				return;
			}
			for (int i = 0; i < k; i++) {
				System.out.print(s);
				System.out.print(" ");
			}
			for (int i = 0; i < n - k - 1; i++) {
				System.out.print(1);
				System.out.print(" ");
			}
			System.out.println(1);
		}
	}
}



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 static 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 || Integer.MAX_VALUE < nl) {
			throw new NumberFormatException();
		}
		return (int) nl;
	}
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}