D. Game With Array

D. Game With Array

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Petya and Vasya are competing with each other in a new interesting game as they always do.

At the beginning of the game Petya has to come up with an array of NN positive integers. Sum of all elements in his array should be equal to SS. Then Petya has to select an integer KK such that 0≤K≤S0≤K≤S.

In order to win, Vasya has to find a non-empty subarray in Petya's array such that the sum of all selected elements equals to either KK or S−KS−K. Otherwise Vasya loses.

You are given integers NN and SS. You should determine if Petya can win, considering Vasya plays optimally. If Petya can win, help him to do that.

Input

The first line contains two integers NN and SS (1≤N≤S≤1061≤N≤S≤106) — the required length of the array and the required sum of its elements.

Output

If Petya can win, print "YES" (without quotes) in the first line. Then print Petya's array in the second line. The array should contain NN positive integers with sum equal to SS. In the third line print KK. If there are many correct answers, you can print any of them.

If Petya can't win, print "NO" (without quotes).

You can print each letter in any register (lowercase or uppercase).

Examples

input

Copy

1 4

output

Copy

YES
4
2

input

Copy

3 4

output

Copy

NO

input

Copy

3 8

output

Copy

YES
2 1 5
4

样例可不是白给的，从看样例到解决问题只需五分钟

根据两个YES和一个NO猜测是m与n是大于二倍关系才能完成表示，并通过手写几个小样例发现确实是这样，而且2倍的时候也能表示

再考虑通解，抓住大于2倍的特点，我们前n-1个全部填上1，剩下全部填上m-(n-1)

再把k选成m/2这样的话，无论怎么表示，要么小于m/2,要么大于m/2

做多了思路自然产生

#include<iostream>
#include<cstdio>
#include<cstring>
# include<iomanip>

#include<algorithm>
#define  mo 998244353;
using namespace std;

typedef long long int ll;


int main()
{

  int n,m;

  cin>>n>>m;

  if(m>=2*n)
  {
      cout<<"YES"<<endl;

      int up=m/2;

      for(int i=1;i<n;i++)
      {
          cout<<1<<" ";
      }
      cout<<m-(n-1)<<endl;

      cout<<m/2<<endl;
  }
  else
  {
      cout<<"NO"<<endl;
  }

    return 0;
}