#include<bits/stdc++.h>
using namespace std;
const int N=5e3+5,mod=998244353;
int tid,n,x,f[N][N],a[N],ans[N],b[N];
int main()
{
	//freopen("story6.in","r",stdin);
	//freopen("story.out","w",stdout);
	scanf("%d %d",&n,&x);
	bool fl1=1;
	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	for(int i=1;i<n;i++)fl1&=(a[i]<=a[i+1]);
	if(fl1)
	{
		f[0][0]=1;
		for(int i=1;i<=n;i++)for(int j=0;j<=i;j++)
		{
			f[i][j]=f[i-1][j];
			if(j>0)
			{
				if(a[i]>=i)f[i][j]=(f[i][j]+1ll*f[i-1][j-1]*(a[i]-j+x))%mod;
				else f[i][j]=(f[i][j]+1ll*f[i-1][j-1]*max(0,a[i]-j+1))%mod;
			}
		}
		for(int i=0;i<=n;i++)printf("%d ",f[n][i]);printf("\n");
		return 0;
	}
	for(int i=1;i<=n;i++)for(int j=1;j<=n;j++)b[j]+=(a[i]>=j);
	for(int i=n;i>=1;i--)
	{
		if(a[i]<b[i] && b[i]>=i)
		{
			for(int j=a[i]+1;j<=b[i];j++)a[j]=b[j];
			a[i]=b[i];
		}
	}
	f[n+1][0]=1;
	for(int i=n;i>=1;i--)for(int j=0;j<=n-i+1;j++)
	{
		f[i][j]=f[i+1][j];
		if(j>0)
		{
			if(a[i]>=i)f[i][j]=(f[i][j]+1ll*f[i+1][j-1]*(a[i]-j+x))%mod;
			else f[i][j]=(f[i][j]+1ll*f[i+1][j-1]*max(0,a[i]-j+1))%mod;
		}
	}
	for(int i=0;i<=n;i++)printf("%d ",f[1][i]);printf("\n");
	return 0;
}