Problem: There are n houses in a row. They are numbered from 1 to n in order from left to right. Initially you are in the house 1.

You have to perform k moves to other house. In one move you go from your current house to some other house. You can't stay where you are (i.e., in each move the new house differs from the current house). If you go from the house x to the house y, the total distance you walked increases by |x-y| units of distance, where |a| is the absolute value of a. It is possible to visit the same house multiple times (but you can't visit the same house in sequence).

Your goal is to walk exactly s units of distance in total.

If it is impossible, print "NO". Otherwise print "YES" and any of the ways to do that. Remember that you should do exactly k moves.

Input

The first line of the input contains three integers n, k, s (2 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5, 1 ≤ s ≤ 10^{18}) — the number of houses, the number of moves and the total distance you want to walk.

Output

If you cannot perform k moves with total walking distance equal to s, print "NO".

Otherwise print "YES" on the first line and then print exactly k integers h_i (1 ≤ h_i ≤ n) on the second line, where h_i is the house you visit on the i-th move.

For each j from 1 to k-1 the following condition should be satisfied: h_j ≠ h_{j + 1}. Also h_1 ≠ 1 should be satisfied.

Examples

Input

10 2 15


Output

YES
10 4 


Input

10 9 45


Output

YES
10 1 10 1 2 1 2 1 6 


Input

10 9 81


Output

YES
10 1 10 1 10 1 10 1 10 


Input

10 9 82


Output

NO

Solution (in JAVA):

Solution:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author wilso
 */
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
public class codeforces {
    static final long MOD2 = 998_244_353;
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter pw = new PrintWriter(System.out);
       
        int tc = 1;
        for (int rep = 0; rep < tc; rep++) {
            long N = sc.nl();
            long k = sc.nl();
            long s = sc.nl();
            if (s%k == 0) {
                if ((s/k)+1> N || k>s) {
                    pw.println("NO");
                }
                else {
                    StringBuilder sb = new StringBuilder();
                    for (int i = 0; i < k; i++) {
                        if (i % 2 == 0) {
                            long x = s/k+1;
                            sb.append(x + " ");
                        }
                        else {
                            sb.append(1 + " ");
                        }
                    }
                    pw.println("YES");
                    pw.println(sb.toString());
                }
            }
            else {
                long a=s/k;
                long x=a*(k-1);
                long bs=s-x;
                long[] arr=new long[(int)k];
                int i=0;
                for(i=0;i<k-1;i++)
                    arr[i]=a;
                arr[(int)(k-1)]=bs;
                long xx=bs-a;
                for(i=0;i<xx;i++)
                    arr[i]++;
                arr[(int)k-1]=a;
                if(arr[0]+1>N || k>s){
                    pw.println("NO");
                }
                else{
                    StringBuilder sb=new StringBuilder();
                    for(i=0;i<xx;i++){
                        if(i%2==0)
                            sb.append((arr[0]+1)+" ");
                        else
                            sb.append(1+" ");
                    }
                    if(xx%2==0){
                        for(i=0;i<k-xx;i++){
                            if(i%2==0) {
                                sb.append((a+1)+" ");
                            }
                            else {
                                sb.append(1+" ");
                            }
                        }
                    }
                    else{
                        for(i=0;i<k-xx;i++){
                            if(i%2==0) {
                                sb.append(2+" ");
                            }
                            else {
                                sb.append((2+a)+" ");
                            }
                        }
                    }
                    pw.println("YES");
                    pw.println(sb.toString());
                }
            
            }
                     
        }
        
        pw.close();
    }
    
    
    static String solve(int n, int t, int k, int[] arr) {
        int ret = n-t;
        if (k > ret) return "-1";
        int[] ref = new int[n];
        int parent = 0;
        int idx = 1;
        for (int i = 0; i < t; i++) {
            int pos = idx;
            for (int j = 0; j < arr[i]; j++) {
                ref[idx] = parent;
                if (ret > k && parent < pos-1) {
                    parent++;
                    if (j+1 < arr[i]) ret--;
                }
                idx++;
            }
            parent = pos;
        }
        if (ret == k) {
            StringBuilder sb = new StringBuilder();
            sb.append(n);
            sb.append("\n");
            for (int i = 1; i < n; i++) {
                sb.append((i+1) + " " + (ref[i] + 1));
//                sb.append(i + " " + ref[i]);
                sb.append("\n");
            }
            return sb.toString();
        }
        else {
            return "-1";
        }
    }
 
    static int summation(int x) {
        return x * (x+1) / 2;
    }  
    static long pow(long num, long exp, long mod){
        long ans=1;
        for(int i=1;i<=exp;i++){
            ans=(ans*num)%mod;
        }
        return ans;
    }
    static boolean isPrime(int n)
    {
 
        if (n <= 1)
            return false;
        else if (n == 2)
            return true;
        else if (n % 2 == 0)
            return false;
        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    static int gcd(int a, int b)
    {
        if (a == 0)
            return b; 
        return gcd(b % a, a); 
    }
    static long gcd(long a, long b) {
        if (a == 0) return b;
        return gcd(b % a, a);
    }
    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }
    public static void sort(int[] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            int temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr);
    }
    public static void sort(long[] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            long temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr);
    }
    static int charint(char c) {
        return Integer.parseInt(String.valueOf(c));
    }
    
    /* */
    //printing methods
    /* */
    //WOW!
    /* */
    public static void printArr(PrintWriter pw, int[] arr) {
        StringBuilder sb = new StringBuilder();
        for (int x : arr) {
            sb.append(x + "");
        }
        sb.setLength(sb.length() - 1);
        pw.println(sb.toString());
    }
    public static void printArr2d(PrintWriter pw, int[][] arr) {
        StringBuilder sb = new StringBuilder();
        for (int[] row : arr) {
            for (int x : row) {
                sb.append(x + " ");
            }
            sb.setLength(sb.length() - 1);
            sb.append("\n");
        }
        pw.println(sb.toString());
    }
}

class FastScanner {
    BufferedReader br;
    StringTokenizer st;

    public FastScanner() {
        br = new BufferedReader(new InputStreamReader(System.in), 32768);
        st = null;
    }

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

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

    int[] intArray(int N) {
        int[] ret = new int[N];
        for (int i = 0; i < N; i++)
            ret[i] = ni();
        return ret;
    }

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

    long[] longArray(int N) {
        long[] ret = new long[N];
        for (int i = 0; i < N; i++)
            ret[i] = nl();
        return ret;
    }

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

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

class MultiSet {
    TreeMap<Long, Integer> map = new TreeMap<>();
    private int size = 0;
    public MultiSet() {
    }
    public void add(Long val) {
        map.put(val, map.getOrDefault(val, 0) + 1);
        size++;
    }
    public void remove(Long val) {
        map.put(val, map.get(val) - 1);
        if (map.get(val) == 0) {
            map.remove(val);
        }
        size--;
    }
    public int size() {
        return size;
    }
    public Long higher(Long val) {
        return map.higherKey(val);
    }
    public Long lower(Long val) {
        return map.lowerKey(val);
    }
    public Long ceiling(Long val) {
        return map.ceilingKey(val);
    }
    public Long floor(Long val) {
        return map.floorKey(val);
    }
    public Long first() {
        return map.firstKey();
    }
    public Long last() {
        return map.lastKey();
    }
    public boolean isEmpty() {
        return map.isEmpty();
    }
}