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:
import java.io.*;
import java.util.*;
import java.lang.*;
import java.util.HashMap;
public class templ implements Runnable {
    class pair
    {
        int v,val;
        pair(int f,int s)
        {
            v=f;
            val=s;
        }
    }
    public static ArrayList<Integer> g[]=new ArrayList[1000000];
    public static int vis[]=new int[1000000];
    public static long M=1000000007;
    static int binarySearch(int arr[], int l, int r, int x)
    {
        if (r >= l)
        {
            int mid = l + (r - l)/2;
            if (arr[mid] == x)
                return mid;
            if (arr[mid] > x)
                return binarySearch(arr, l, mid-1, x);
            return binarySearch(arr, mid+1, r, x);
        }
        return -1;
    }
    void merge1(int arr[], int l, int m, int r)
    {
        int n1 = m - l + 1;
        int n2 = r - m;
        int L[] = new int [n1];
        int R[] = new int [n2];
        for (int i=0; i<n1; ++i)
            L[i] = arr[l + i];
        for (int j=0; j<n2; ++j)
            R[j] = arr[m + 1+ j];
        int i = 0, j = 0;
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i]<=R[j])
            {
                arr[k] = L[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                j++;
            }
            k++;
        }
        while (i < n1)
        {
            arr[k] = L[i];
            i++;
            k++;
        }
        while (j < n2)
        {
            arr[k] = R[j];
            j++;
            k++;
        }
    }
    void sort1(int arr[], int l, int r)
    {
        if (l < r)
        {
            int m = (l+r)/2;
            sort1(arr, l, m);
            sort1(arr , m+1, r);
            merge1(arr, l, m, r);
        }
    }
    void merge3(int arr[],int arr1[],int arr2[], int l, int m, int r)
    {
        int n1 = m - l + 1;
        int n2 = r - m;
        int L[] = new int [n1];
        int R[] = new int [n2];
        int L1[]=new int[n1];
        int R1[]=new int[n2];
        int L2[]=new int[n1];
        int R2[]=new int[n2];
        //long L3[]=new long[n1];
        //long R3[]=new long[n2];
        for (int i=0; i<n1; ++i)
        {
            L[i] = arr[l + i];
            L1[i]=arr1[l+i];
            L2[i]=arr2[l+i];
            //L3[i]=arr3[l+i];
        }
        for (int j=0; j<n2; ++j)
        {
            R[j] = arr[m + 1+ j];
            R1[j]=arr1[m+1+j];
            R2[j]=arr2[m+1+j];
            //R3[j]=arr3[m+1+j];
        }
        int i = 0, j = 0;
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i] <= R[j])
            {
                arr[k] = L[i];
                arr1[k]=L1[i];
                arr2[k]=L2[i];
                //arr3[k]=L3[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                arr1[k]=R1[j];
                arr2[k]=R2[j];
                //arr3[k]=R3[j];
                j++;
            }
            k++;
        }
        while (i < n1)
        {
            arr[k] = L[i];
            arr1[k]=L1[i];
            arr2[k]=L2[i];
            //arr3[k]=L3[i];
            i++;
            k++;
        }
        while (j < n2)
        {
            arr[k] = R[j];
            arr1[k]=R1[j];
            arr2[k]=R2[j];
            //arr3[k]=R3[j];
            j++;
            k++;
        }
    }
    void sort3(int arr[],int arr1[],int arr2[], int l, int r)
    {
        if (l < r)
        {
            int m = (l+r)/2;
            sort3(arr,arr1,arr2, l, m);
            sort3(arr ,arr1,arr2, m+1, r);
            merge3(arr,arr1,arr2,l, m, r);
        }
    }
    void merge2(int arr[],int arr1[],int l, int m, int r)
    {
        int n1 = m - l + 1;
        int n2 = r - m;
        int L[] = new int [n1];
        int R[] = new int [n2];
        int L1[]=new int[n1];
        int R1[]=new int[n2];
        for (int i=0; i<n1; ++i)
        {
            L[i] = arr[l + i];
            L1[i]=arr1[l+i];
        }
        for (int j=0; j<n2; ++j)
        {
            R[j] = arr[m + 1+ j];
            R1[j]=arr1[m+1+j];
        }
        int i = 0, j = 0;
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i] <= R[j])
            {
                arr[k] = L[i];
                arr1[k]=L1[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                arr1[k]=R1[j];
                j++;
            }
            k++;
        }
        while (i < n1)
        {
            arr[k] = L[i];
            arr1[k]=L1[i];
            i++;
            k++;
        }
        while (j < n2)
        {
            arr[k] = R[j];
            arr1[k]=R1[j];
            j++;
            k++;
        }
    }
    void sort2(int arr[],int arr1[],int l, int r)
    {
        if (l < r)
        {
            int m = (l+r)/2;
            sort2(arr,arr1, l, m);
            sort2(arr ,arr1, m+1, r);
            merge2(arr,arr1,l, m, r);
        }
    }
    void merge4(int arr[],int arr1[],int arr2[],int arr3[], int l, int m, int r)
    {
        int n1 = m - l + 1;
        int n2 = r - m;
        int L[] = new int [n1];
        int R[] = new int [n2];
        int L1[]=new int[n1];
        int R1[]=new int[n2];
        int L2[]=new int[n1];
        int R2[]=new int[n2];
        int L3[]=new int[n1];
        int R3[]=new int[n2];
        for (int i=0; i<n1; ++i)
        {
            L[i] = arr[l + i];
            L1[i]=arr1[l+i];
            L2[i]=arr2[l+i];
            L3[i]=arr3[l+i];
        }
        for (int j=0; j<n2; ++j)
        {
            R[j] = arr[m + 1+ j];
            R1[j]=arr1[m+1+j];
            R2[j]=arr2[m+1+j];
            R3[j]=arr3[m+1+j];
        }
        int i = 0, j = 0;
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i] <= R[j])
            {
                arr[k] = L[i];
                arr1[k]=L1[i];
                arr2[k]=L2[i];
                arr3[k]=L3[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                arr1[k]=R1[j];
                arr2[k]=R2[j];
                arr3[k]=R3[j];
                j++;
            }
            k++;
        }
        while (i < n1)
        {
            arr[k] = L[i];
            arr1[k]=L1[i];
            arr2[k]=L2[i];
            arr3[k]=L3[i];
            i++;
            k++;
        }
        while (j < n2)
        {
            arr[k] = R[j];
            arr1[k]=R1[j];
            arr2[k]=R2[j];
            arr3[k]=R3[j];
            j++;
            k++;
        }
    }
    void sort4(int arr[],int arr1[],int arr2[],int arr3[], int l, int r)
    {
        if (l < r)
        {
            int m = (l+r)/2;
            sort4(arr,arr1,arr2,arr3, l, m);
            sort4(arr ,arr1,arr2,arr3, m+1, r);
            merge4(arr,arr1,arr2,arr3,l, m, r);
        }
    }
    public int justsmall(int a[],int l,int r,int x)
    {
        int p=-1;
        while(l<=r)
        {
            int mid=(l+r)/2;
            if(a[mid]<=x)
            {
                p=mid;
                l=mid+1;
            }
            else
                r=mid-1;
        }
        return p;
    }
    public int justlarge(int a[],int l,int r,int x)
    {
        int p=0;
        while(l<=r)
        {
            int mid=(l+r)/2;
            if(a[mid]<=x)
            {
                l=mid+1;
            }
            else
            {
                p=a[mid];
                r = mid - 1;
            }
        }
        return p;
    }
    long gcd(long x,long y)
    {
        if(x%y==0)
            return y;
        else
            return(gcd(y,x%y));
    }
    long fact(long n)
    {
        long ans=1;
        for(int i=1;i<=n;i++)
            ans*=i;
        return ans;
    }
    public static void main(String args[])throws Exception
    {
        new Thread(null,new templ(),"templ",1<<26).start();
    }
    public void run() {
        try
        {
            InputReader in = new InputReader(System.in);
            PrintWriter out = new PrintWriter(System.out);
            int n=in.ni();
            int k=in.ni();
            long s=in.nl();
            if(s<k||((long)n-1)*(long)k<s)
                out.println("NO");
            else
            {
                out.println("YES");
                long a[]=new long[k];
                for(int i=0;i<k;i++)
                {
                    double x=(double)s/(k-i);
                    long y=(long)Math.ceil(x);
                    s-=y;
                    a[i]=y;
                }
                long prev=1;
                for(int i=0;i<k;i++)
                {
                    if(prev+a[i]>n)
                    {
                        out.print(prev-a[i]+" ");
                        prev=prev-a[i];
                    }
                    else
                    {
                        prev=prev+a[i];
                        out.print(prev+" ");
                    }
                }
            }
            out.close();
        }
        catch(Exception e){
            return;
        }
    }
    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

    }
}