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 PYTHON3):

Solution:
from __future__ import print_function
import sys
import math
import os.path
from copy import deepcopy
from functools import reduce


from collections import Counter, ChainMap, defaultdict
from itertools import cycle, chain
from queue import Queue, PriorityQueue, deque
from heapq import heappush, heappop, heappushpop, heapify, heapreplace, nlargest, nsmallest
import bisect

from statistics import mean, mode, median, median_low, median_high


# CONFIG
sys.setrecursionlimit(10**9)

# LOG 
def log(*args, **kwargs):
    print(*args, file=sys.stderr, **kwargs)


# INPUT
def ni():
    return map(int, input().split())


def nio(offset):
    return map(lambda x: int(x) + offset, input().split())


def nia():
    return list(map(int, input().split()))


# CONVERT
def toString(aList, sep=" "):
    return sep.join(str(x) for x in aList)


def toMapInvertIndex(aList):
    return {k: v for v, k in enumerate(aList)}


# SORT
def sortId(arr):
    return sorted(range(len(arr)), key=lambda k: arr[k])


# MAIN

n,k,s = ni()

if s > (n-1)*k:
    print("NO")
elif s < k:
    print("NO")
else:
    print("YES")
    sodu = s % k
    sochia = s // k

    # print(sochia, sodu)

    res = [0]*k
    des = 1+sochia+sodu
    deb = 0
    if (des > n):
       deb = des - n
       des = n 
    res[0]= des 
    direct = 1
    for i in range(1,k):
        direct *= -1
        move = sochia + deb
        deb = 0
        if (move > n-1):
            deb = move - (n-1)
            move = n-1
        des += move*direct
        res[i] = des
    print(toString(res))