#include<bits/stdc++.h>

#define ll long long
#define mk make_pair
#define fi first
#define se second
#define int long long

using namespace std;

inline ll read(){
	ll x=0,f=1;char c=getchar();
	for(;(c<'0'||c>'9');c=getchar()){if(c=='-')f=-1;}
	for(;(c>='0'&&c<='9');c=getchar())x=x*10+(c&15);
	return x*f;
}

template<typename T>void cmax(T &x,T v){x=max(x,v);}
template<typename T>void cmin(T &x,T v){x=min(x,v);}

int n;ll k;

namespace Solve1{

ll f[105][10005];
void solve(){
	int tar=n*(n-1)/4,cur=0;
	vector<int>vis(n+1);
	auto calc=[&](){
		int cnt=0,tot=0;
		for(int i=1;i<=n;i++){
			if(vis[i])tot+=cnt;
			else cnt++;
		}
		return tot;
	};
	
	f[0][0]=1;
	for(int i=1;i<=n;i++){
		for(int j=0;j<=i*(i-1)/2;j++){
			for(int x=0;x<=min(i-1,j);x++)f[i][j]=min(k+1,f[i][j]+f[i-1][j-x]);
		}
	}
	
	vector<int>ans(n+1);
	for(int i=1;i<=n;i++){
		for(int j=1;j<=n;j++)if(!vis[j]){
			int cnt=cur;
			for(int k=j+1;k<=n;k++)if(vis[k])cnt++;
			vis[j]=1,cnt+=calc();
			if(cnt>tar){
				vis[j]=0;continue;
			}
			ll ways=f[n-i][tar-cnt];
			if(ways<k){
				k-=ways,vis[j]=0;
				continue;
			}
			else{
				ans[i]=j;
				for(int k=j+1;k<=n;k++)if(vis[k])cur++;
				break;				
			}
		}
		if(ans[i]==0)return puts("NO"),void();
	}
	
	puts("YES");
	for(int i=1;i<=n;i++)cout<<ans[i]<<" \n"[i==n];
}

}

namespace Solve2{

const int N=3e5+5;
const int D=20;
ll f[N][D];
__int128 sum[N][D];

struct BIT{
	int c[N];
	int lowbit(int x){return x&(-x);}
	void add(int x,int v){for(int i=x;i<=n;i+=lowbit(i))c[i]+=v;}
	int qsum(int x){int res=0;for(int i=x;i;i-=lowbit(i))res+=c[i];return res;}
}T;

void solve(){
	f[0][0]=1;for(int j=0;j<D;j++)sum[0][j]=1;
	for(int i=1;i<=n;i++){
		for(int j=0;j<D;j++){
			if(j<=i-1)f[i][j]=min(sum[i-1][j],(__int128)(k)+1);
			else f[i][j]=min(sum[i-1][j]-sum[i-1][j-i],(__int128)(k)+1);
		}
		sum[i][0]=f[i][0];
		for(int j=1;j<D;j++)sum[i][j]=sum[i][j-1]+f[i][j];
	}
	
	auto getans=[&](int n,int tar,ll K){
		vector<int>ans(n+1);
		set<int>S;
		for(int i=1;i<=n;i++)S.insert(i);
		ll cur=0;
		for(int i=1;i<=n;i++){
			int L=1,R=n,lim=n;
			while(L<=R){
				int j=(L+R)>>1;
				if(cur+n-j-(i-1-T.qsum(j-1))>tar)L=j+1;
				else R=j-1,lim=j;
			}
			for(auto it=S.lower_bound(lim);it!=S.end();++it){
				int j=(*it);
				ll cnt=cur+n-j-(i-1-T.qsum(j-1));
				if(cnt>tar)continue;
				ll ways=f[n-i][tar-cnt];
				if(ways<K){K-=ways;continue;}
				else{
					ans[i]=j,cur=cnt,S.erase(S.find(j)),T.add(j,1);
					break;				
				}
			}
		}
		return ans;
	};
	
	auto hav=[&](int i){return 1ll*i*(i-1)/2+1ll*i*(n-i);};
	ll tar=1ll*n*(n-1)/4;int p=0;
	for(int i=1;i<=n;i++)if(hav(i)<=tar)p=i;
	
	vector<int>ans(n+1);
	for(int i=1;i<=p;i++)ans[i]=i;
	
	int ret=0;
	for(int i=0;i<D;i++){
		if(k<=f[n-p-1][i]){ret=i;break;}
		k-=f[n-p-1][i];
	}
	int cc=tar-hav(p);
	ans[p+1]=n-cc+ret;
	
	auto vec=getans(n-p-1,ret,k);
	vector<int>id(n+1),vis(n+1);
	for(int i=1;i<=p+1;i++)vis[ans[i]]=1;
	int cnt=0;
	for(int i=1;i<=n;i++){
		if(vis[i]==1)continue;
		id[++cnt]=i;
	}
	for(int i=1;i<=n-p-1;i++)ans[i+p+1]=id[vec[i]];
	
	puts("YES");
	for(int i=1;i<=n;i++)cout<<ans[i]<<" \n"[i==n];
}

}

signed main(void){

#ifndef ONLINE_JUDGE
	freopen("in.in","r",stdin);
#endif

	n=read(),k=read();
	if(n%4==2||n%4==3)return puts("NO"),0;
	if(n<=80)return Solve1::solve(),0;
	else return Solve2::solve(),0;

	return 0;
}