Problem: This is the hard version of the problem. The only difference between the easy version and the hard version is the constraints on n. You can only make hacks if both versions are solved.

A permutation of 1, 2, …, n is a sequence of n integers, where each integer from 1 to n appears exactly once. For example, [2,3,1,4] is a permutation of 1, 2, 3, 4, but [1,4,2,2] isn't because 2 appears twice in it.

Recall that the number of inversions in a permutation a_1, a_2, …, a_n is the number of pairs of indices (i, j) such that i < j and a_i > a_j.

Let p and q be two permutations of 1, 2, …, n. Find the number of permutation pairs (p,q) that satisfy the following conditions:

  * p is lexicographically smaller than q. 
  * the number of inversions in p is greater than the number of inversions in q. 



Print the number of such pairs modulo mod. Note that mod may not be a prime.

Input

The only line contains two integers n and mod (1≤ n≤ 500, 1≤ mod≤ 10^9).

Output

Print one integer, which is the answer modulo mod.

Example

Input


4 403458273


Output


17

Note

The following are all valid pairs (p,q) when n=4.

  * p=[1,3,4,2], q=[2,1,3,4], 
  * p=[1,4,2,3], q=[2,1,3,4], 
  * p=[1,4,3,2], q=[2,1,3,4], 
  * p=[1,4,3,2], q=[2,1,4,3], 
  * p=[1,4,3,2], q=[2,3,1,4], 
  * p=[1,4,3,2], q=[3,1,2,4], 
  * p=[2,3,4,1], q=[3,1,2,4], 
  * p=[2,4,1,3], q=[3,1,2,4], 
  * p=[2,4,3,1], q=[3,1,2,4], 
  * p=[2,4,3,1], q=[3,1,4,2], 
  * p=[2,4,3,1], q=[3,2,1,4], 
  * p=[2,4,3,1], q=[4,1,2,3], 
  * p=[3,2,4,1], q=[4,1,2,3], 
  * p=[3,4,1,2], q=[4,1,2,3], 
  * p=[3,4,2,1], q=[4,1,2,3], 
  * p=[3,4,2,1], q=[4,1,3,2], 
  * p=[3,4,2,1], q=[4,2,1,3]. 

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define pb push_back
typedef long long ll;
//mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
long long t,n,m,k,ccnt,pos=0,sum=0,minn2=INT_MAX,sum2,cnt=0,cnt1=0,cnt2=0,cnt3=0,cnt4=0,cnt5=0,cnt6=0,cnt7=0,a[1000005],x1,y7,x2,y2,x3,y3,bbb;
long long b[1000005],c[1000005],x,y,z,d=0,l2,r2,temcnt,le[200005],ri[200005];
//long long c3[2005][2005],c4[1000005],kk[1000005];
long long pos1=0,pos2=0,tem,tem2,l,r,ans=0,mod=998244353,tw[100005],th[100005],ee,loc[1000005],te[100005],vis[1000005],ans1[100005],ans2[100005];
long long minn=LONG_LONG_MAX,maxx=-LONG_LONG_MAX,maxx2,posb,mid,mxl[100005],mxr[100005],mnl[100005],mnr[100005],mx[100005],mn[100005],plmx[100005],prmx[100005],plmn[100005],prmn[100005];
ll c10,c11,c20,c21,dp[505][505][2],dp2[505][505][2],prec[1000000];
long double dd[10005],aaa,nn;
string s1,s2,s;
char ch,ch2,cc[1005][1005],cc2[1005][1005];
vector<ll> v[1000005];
pair<ll,ll> p[505];
map<pair<ll,ll>,ll> mp;
long long fpow(long long aa,long long bb)
{
    if(bb==0)
    {
        return 1;
    }
    else if(bb<0)
    {
        return 0;
    }
    long long kk1=aa;
    long long kk2=1;
    while(bb>1)
    {
        if(bb%2)
        {
            kk2*=kk1;
            kk2%=mod;
        }
        kk1*=kk1;
        kk1%=mod;
        bb=bb/2;
    }
    return (kk1*kk2)%mod;
}
long long co(long long x,long long y)
{
    long long ans=1;
    long long ans2=1;
    if(x==y||y==0)
    {
        return 1;
    }
    else
    {
        for(int i=x-y+1;i<=x;i++)
        {
            ans=ans*i;
            ans=ans%mod;
        }
        for(int i=1;i<=y;i++)
        {
            ans2=ans2*i;
            ans2=ans2%mod;
        }
        ans2=fpow(ans2,mod-2);
        ans2=(ans2*ans)%mod;
        return ans2;
    }
}
int summ(ll x)
{
    //cout<<"! "<<x<<'\n';
    ll ans=0,pos=0;
    ll maxx;
    x++;
    ll xx=x;

    for(int i=0;;i++)
    {
        if(tw[i]>x)
        {
            maxx=i;
            break;
        }
    }
    //cout<<"???????? "<<maxx<<'\n';
    for(int i=maxx-1;i>=0;i--)
    {
        if(xx>=tw[i])
        {
            th[i]=1;
            xx-=tw[i];
        }
        else
        {
            th[i]=0;
        }
    }
    /*for(int i=maxx-1;i>=0;i--)
    {
        cout<<th[i];
    }
    cout<<'\n';*/
    for(int i=maxx-1;i>=0;i--)
    {
        if(th[i])
        {
            ans+=v[i][pos];
            pos=2*pos+2;
        }
        else
        {
            pos*=2;
        }
    }
    return ans;
}
void modify(ll x,ll m)
{
    v[0][x]+=m;
    for(int i=1;i<cnt2;i++)
    {
        v[i][x/2]+=m;
        x/=2;
    }
}
void dfs(ll y)
{
    //cout<<y<<" ";
    a[y]=cnt;
    vis[y]=1;
    for(int i=0;i<v[y].size();i++)
    {
        if(vis[v[y][i]]==0)
        {
            //dp[x][v[y][i]]=dp[x][y]+1;
            dfs(v[y][i]);
        }
    }
}
signed main()
{
    cin.tie(0);
    cout.tie(0);
    ios_base::sync_with_stdio(0);
    //cout<<fixed<<setprecision(20);
    cin>>n>>mod;
    if(n<=3)
    {
        cout<<0;
    }
    else
    {
        a[0]=1;
        a[1]=2;
        a[2]=2;
        a[3]=1;
        b[3]=0;
        for(int i=4;i<=n;i++)
        {
            b[i]=b[i-1]*i;
            b[i]%=mod;
            ans1[0]=1;
            if(mod==1)
            {
                ans1[0]=0;
            }
            cnt1=(i-1)*(i-2)/2;
            cnt2=i*(i-1)/2;
            for(int j=1;j<=cnt1;j++)
            {
                ans1[j]=ans1[j-1]+a[j];
                ans1[j]%=mod;
            }
            c[0]=ans1[0];
            for(int j=1;j<=cnt1;j++)
            {
                c[j]=c[j-1]+ans1[j];
                c[j]%=mod;
            }
            prec[0]=c[0];
            for(int j=1;j<=cnt1;j++)
            {
                prec[j]=prec[j-1]+c[j];
                prec[j]%=mod;
            }
            for(int j=2;j<=cnt1;j++)
            {
                if(j==2)
                {
                    //cout<<j<<" "<<a[j]<<" "<<c[0]*(i-1)<<'\n';
                    b[i]+=(a[j]*c[0]*(i-1));
                    b[i]%=mod;
                }
                else
                {
                    y=j-i-1;
                    if(y<=0)
                    {
                        z=c[j-2]*(i-1)-(prec[j-3]);
                    }
                    else
                    {
                        z=c[j-2]*(i-1)-(prec[j-3]-prec[y-1]);
                    }

                    //cout<<j<<" "<<a[j]<<" "<<z<<'\n';
                    z%=mod;
                    z*=a[j];
                    z%=mod;
                    if(z<0)
                    {
                        z+=mod;
                    }
                    b[i]+=z;
                    b[i]%=mod;
                }

            }
            for(int j=0;j<=i*(i-1)/2;j++)
            {
                x=j-i+1;
                y=j;
                if(x<0)
                {
                    x=0;
                }
                if(y>cnt1)
                {
                    y=cnt1;
                }
                if(x==0)
                {
                    a[j]=ans1[y];
                }
                else
                {
                    a[j]=(ans1[y]-ans1[x-1]+mod)%mod;
                }
                //cout<<a[j]<<" ";
            }
            //cout<<'\n';
        }
        cout<<b[n];
    }



}