codeforces 1015D

D. Walking Between Houses

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

There are $\mathrm{nn houses\; in\; a\; row.\; They\; are\; numbered\; from 11 to nn in\; order\; from\; left\; to\; right.\; Initially\; you\; are\; in\; the\; house 11.}$

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

Your goal is to walk exactly $\mathrm{ss units\; of\; distance\; in\; total.}$

If it is impossible, print "NO". Otherwise print "YES" and any of the ways to do that. Remember that you should do exactly $\mathrm{kk moves.}$

Input

The first line of the input contains three integers $\mathrm{nn, kk, ss (2\le n\le 1092\le n\le 109, 1\le k\le 2\cdot 1051\le k\le 2\cdot 105, 1\le s\le 10181\le s\le 1018)\; —\; the\; number\; of\; houses,\; the\; number\; of\; moves\; and\; the\; total\; distance\; you\; want\; to\; walk.}$

Output

If you cannot perform $\mathrm{kk moves\; with\; total\; walking\; distance\; equal\; to ss,\; print\; "NO".}$

Otherwise print "YES" on the first line and then print exactly $\mathrm{kk integers hihi (1\le hi\le n1\le hi\le n)\; on\; the\; second\; line,\; where hihi is\; the\; house\; you\; visit\; on\; the ii-th\; move.}$

For each $\mathrm{jj from 11 to k-1k-1 the\; following\; condition\; should\; be\; satisfied: hj\ne hj+1hj\ne hj+1.\; Also h1\ne 1h1\ne 1 should\; be\; satisfied.}$

Examples

input

Copy

10 2 15

output

Copy

YES
10 4 

input

Copy

10 9 45

output

Copy

YES
10 1 10 1 2 1 2 1 6 

input

Copy

10 9 81

output

Copy

YES
10 1 10 1 10 1 10 1 10 

input

Copy

10 9 82

output

Copy

NO

题意：在长度为1~n的路径上，要求你走k次，要求一共走的距离为s
题解：如果可以走的话就走min(n - 1,s - (k-i))的距离，然后循环走就行
代码如下：

#include <map>
#include <set>
#include <cmath>
#include <ctime>
#include <stack>
#include <queue>
#include <cstdio>
#include <cctype>
#include <bitset>
#include <string>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <functional>
#define fuck(x) cout<<"["<<x<<"]";
#define FIN freopen("input.txt","r",stdin);
#define FOUT freopen("output.txt","w+",stdout);
//#pragma comment(linker, "/STACK:102400000,102400000")
using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int maxn = 1e5+5;
int ans[maxn];

int main(){
#ifndef ONLINE_JUDGE
  FIN
#endif
  long long n, k, s;
  cin >> n >> k >> s;
  if (s>(n-1)*k){
    cout << "NO" << endl;
    return 0;
  }
  if (s < k) {
    cout << "NO" << endl;
    return 0;
  }
  cout << "YES" << endl;
  long long fsts = 1;
  for (int i=1;i<=k;i++) {
    long long temp = min(n - 1,s - (k-i));
    s -= temp;
    if (fsts == 1) fsts+=temp;
    else fsts-=temp;
    cout << fsts << ' ';
  }
  puts("");
  return 0;

}