Problem:
Score : 400 points

Problem Statement

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

Sample Input 1

4 2 3

Sample Output 1

1 2 3 4

Two pairs (l, r) = (1, 2) and (3, 3) satisfy the condition in the statement.

Sample Input 2

5 3 100

Sample Output 2

50 50 50 30 70

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

#define ll long long
#define INF 99999999
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(),(x).end()

int main()
{
    ll N,K,S;
    cin >> N >> K >> S;
    vector<ll> ans(N,S);

    if( S == 1000000000 )
    {
        if( K == 0 )
        {
            vector<ll> ans2(N,S+1);
            rep(i,ans2.size())
            {
                cout << ans2[i];
                if( i + 1 != ans2.size()) cout << " ";
            }
            cout << endl;
            return 0;
        }
        else
        {
            ll key = 0;
            ll tmp = 0;
            for( ll i = 0;i < N;i++ )
            {
                key++;
                if( tmp == N-K )
                {
                    break;
                }
                if( key == S )
                {
                    key = 0;
                    continue;
                }
                ans[i] = 1;
                tmp++;
            }
        }
    }
    else if( S == 2 )
    {
        rep(i,N-K) ans[i] = S+1;
    }
    else
    {
        rep(i,N-K) ans[i] = S-1;
    }

    rep(i,ans.size())
    {
        cout << ans[i];
        if( i + 1 != ans.size()) cout << " ";
    }
    cout << endl;
}