#include<iostream>
#include<cstdio>
#include<vector>
#include<algorithm>
#define N 200000
#define K 19
#define M 524288
#define mod 998244353
#define g 3
using namespace std;
int read()
{
	char c=0;
	int sum=0;
	while (c<'0'||c>'9') c=getchar();
	while ('0'<=c&&c<='9') sum=sum*10+c-'0',c=getchar();
	return sum;
}
int fast_pow(int a,int b)
{
	int res=1,mul=a;
	while (b)
	{
		if (b&1) res=1ll*res*mul%mod;
		mul=1ll*mul*mul%mod,b>>=1;
	}
	return res;
}
void Adder(int &x,int d)
{
	x=x+d>=mod?x+d-mod:x+d;
	return;
}
void Adder2(int &x,int d)
{
	x=x+d<0?x+d+mod:x+d;
	return;
}
int MD(int x)
{
	return x>=mod?x-mod:x;
}
int MD2(int x)
{
	return x<0?x+mod:x;
}
int n,y,length,a[N+1],ans[N+1],num[M+1],A[M+1],B[M+1],rev[M+1],wn[K+1][M+1],wn2[K+1][M+1];
void NTT(int limit,int *s,int type)
{
	int s1,s2;
	for (int i=1;i<limit;++i) rev[i]=(rev[i>>1]>>1)|((i&1)?limit>>1:0);
	for (int i=0;i<limit;++i)
		if (rev[i]>i)
			swap(s[i],s[rev[i]]);
	if (type==1)
	{
		for (int i=2;i<=limit;i<<=1)
			for (int j=0;j+i-1<limit;j+=i)
				for (int k=j;k<(j|(i>>1));++k)
					s1=s[k],s2=1ll*s[k|(i>>1)]*wn[num[i]][k-j]%mod,s[k]=MD(s1+s2),s[k+(i>>1)]=MD2(s1-s2);
	}
	else
	{
		for (int i=2;i<=limit;i<<=1)
			for (int j=0;j+i-1<limit;j+=i)
				for (int k=j;k<(j|(i>>1));++k)
					s1=s[k],s2=1ll*s[k|(i>>1)]*wn2[num[i]][k-j]%mod,s[k]=MD(s1+s2),s[k+(i>>1)]=MD2(s1-s2);
		s1=fast_pow(limit,mod-2);
		for (int i=0;i<=limit;++i) s[i]=1ll*s[i]*s1%mod;
	}
	return;
}
vector<int>operator * (vector<int>a,vector<int>b)
{
	if (a.empty()) return a;
	if (b.empty()) return b;
	vector<int>c(a.size()+b.size()-1);
	if (min(a.size(),b.size())<=50)
	{
		for (int i=0;i<a.size();++i)
			for (int j=0;j<b.size();++j)
				Adder(c[i+j],1ll*a[i]*b[j]%mod);
		return c;
	}
	int limit=1;
	while (limit<=a.size()+b.size()) limit<<=1;
	for (int i=0;i<=limit;++i) A[i]=B[i]=0;
	for (int i=0;i<a.size();++i) A[i]=a[i];
	for (int i=0;i<b.size();++i) B[i]=b[i];
	NTT(limit,A,1),NTT(limit,B,1);
	for (int i=0;i<=limit;++i) A[i]=1ll*A[i]*B[i]%mod;
	NTT(limit,A,-1);
	for (int i=0;i<c.size();++i) c[i]=A[i];
	return c;
}
vector<int>operator / (vector<int>a,vector<int>b)
{
	vector<int>c(a.size()-b.size()+1);
	if (min(b.size(),c.size())<=50)
	{
		for (int i=0;i<c.size();++i)
			for (int j=0;j<b.size();++j)
				Adder(c[i],1ll*b[j]*a[i+j]%mod);
		return c;
	}
	int limit=1;
	while (limit<=a.size()) limit<<=1;
	for (int i=0;i<=limit;++i) A[i]=B[i]=0;
	for (int i=0;i<a.size();++i) A[i]=a[i];
	for (int i=0;i<b.size();++i) B[b.size()-i]=b[i];
	NTT(limit,A,1),NTT(limit,B,1);
	for (int i=0;i<=limit;++i) A[i]=1ll*A[i]*B[i]%mod;
	NTT(limit,A,-1);
	for (int i=0;i<c.size();++i) c[i]=A[b.size()+i];
	return c;
}
vector<int>operator ^ (vector<int>a,vector<int>b)
{
	vector<int>c(a.size());
	if (min(b.size(),c.size())<=50)
	{
		for (int i=0;i<c.size();++i)
			for (int j=0;j<b.size()&&i+j<a.size();++j)
				Adder(c[i],1ll*b[j]*a[i+j]%mod);
		return c;
	}
	int limit=1;
	while (limit<=a.size()+b.size()) limit<<=1;
	for (int i=0;i<=limit;++i) A[i]=B[i]=0;
	for (int i=0;i<a.size();++i) A[i]=a[i];
	for (int i=0;i<b.size();++i) B[b.size()-i]=b[i];
	NTT(limit,A,1),NTT(limit,B,1);
	for (int i=0;i<=limit;++i) A[i]=1ll*A[i]*B[i]%mod;
	NTT(limit,A,-1);
	for (int i=0;i<c.size();++i) c[i]=A[b.size()+i];
	return c;
}
void calc_inv(int len,int *s1,int *s2)
{
	if (len==1)
	{
		s2[0]=fast_pow(s1[0],mod-2);
		return;
	}
	int limit=1;
	while (limit<=(len<<1)) limit<<=1;
	calc_inv((len+1)>>1,s1,s2);
	int s3[limit+1];
	for (int i=0;i<=limit;++i) s2[i]=(i<((len+1)>>1))?s2[i]:0,s3[i]=(i<len)?s1[i]:0;
	NTT(limit,s2,1),NTT(limit,s3,1);
	for (int i=0;i<=limit;++i) s2[i]=MD2(2ll*s2[i]%mod-1ll*s2[i]*s2[i]%mod*s3[i]%mod);
	NTT(limit,s2,-1);
	for (int i=0;i<=limit;++i) s2[i]=(i<len)?s2[i]:0;
	return;
}
vector<int>get_inv(int len,vector<int>p)
{
	vector<int>v(len);
	for (int i=0;i<min(len,(int)(p.size()));++i) A[i]=p[i];
	calc_inv(len,A,B);
	for (int i=0;i<len;++i) v[i]=B[i];
	return v;
}
vector<int>solve(int l,int r)
{
	if (l==r) return {1,a[l]};
	int mid=(l+r)>>1;
	return solve(l,mid)*solve(mid+1,r);
}
struct seg
{
	struct node
	{
		int l,r;
		vector<int>data;
	};
	node tree[(N<<2)+1];
	void push_up(int k)
	{
		tree[k].data=tree[k<<1].data*tree[k<<1|1].data;
		return;
	}
	void build(int k,int l,int r)
	{
		tree[k].l=l,tree[k].r=r;
		if (l==r)
		{
			tree[k].data={1,MD2(-l)};
			return;
		}
		int mid=(l+r)>>1;
		build(k<<1,l,mid),build(k<<1|1,mid+1,r),push_up(k);
		return;
	}
	void solve(int k,vector<int>p)
	{
		if (tree[k].l==tree[k].r)
		{
			ans[tree[k].l]=p[0];
			return;
		}
		int mid=(tree[k].l+tree[k].r)>>1;
		vector<int>p1=p/tree[k<<1|1].data;
		vector<int>p2(tree[k].r-mid);
		for (int i=0;i<p2.size();++i) p2[i]=p[i+mid-tree[k].l+1];
		solve(k<<1,p1),solve(k<<1|1,p2);
		return;
	}
};
seg T;
int b[N+1];
int main()
{
	vector<int>p;
	bool op=1;
	for (int i=2,w;i<=M;i<<=1)
	{
		num[i]=++length,w=fast_pow(g,(mod-1)/i);
		for (int j=0,res=1;j<(i>>1);++j,res=1ll*res*w%mod) wn[num[i]][j]=res;
		w=fast_pow(g,(mod-1)/i*(i-1));
		for (int j=0,res=1;j<(i>>1);++j,res=1ll*res*w%mod) wn2[num[i]][j]=res;
	}
	n=read(),y=read();
	for (int i=1;i<=n;++i) a[i]=read(),op&=(a[i-1]<=a[i]);
	if (op)
	{
		for (int i=1;i<=n;++i)
			if (a[i]>=i)
				Adder(a[i],y-1);
		for (int i=1;i<=n;++i) a[i]=MD2(a[i]-i+1);
		p=solve(1,n),T.build(1,0,n),reverse(p.begin(),p.end());
		p=p^get_inv(n+1,T.tree[1].data),p.resize(n+1),T.solve(1,p);
		for (int i=0;i<=n;++i) printf("%d ",ans[n-i]);
		puts("");
	}
	else
	{
		for (int i=1;i<=n;++i) b[a[i]]++;
		for (int i=n-1;i>=1;--i) b[i]+=b[i+1];
		for (int i=1;i<=n;++i)
		{
			if (a[i]>=i) a[i]=max(a[i],b[i]);
			else a[i]=min(a[i],b[i]);
		}
		reverse(a+1,a+n+1);
		for (int i=1;i<=n;++i)
			if (a[i]>=n-i+1)
				Adder(a[i],y-1);
		for (int i=1;i<=n;++i) a[i]=MD2(a[i]-i+1);
		p=solve(1,n),T.build(1,0,n),reverse(p.begin(),p.end());
		p=p^get_inv(n+1,T.tree[1].data),p.resize(n+1),T.solve(1,p);
		for (int i=0;i<=n;++i) printf("%d ",ans[n-i]);
		puts("");
	}
	return 0;
}