Problem:
Score : 1200 points

Problem Statement

N problems have been chosen by the judges, now it's time to assign scores to them!

Problem i must get an integer score A_i between 1 and N, inclusive.
The problems have already been sorted by difficulty: A_1 \le A_2 \le \ldots \le A_N must hold.
Different problems can have the same score, though.

Being an ICPC fan, you want contestants who solve more problems to be ranked higher.
That's why, for any k (1 \le k \le N-1), you want the sum of scores of any k problems to be strictly less than the sum of scores of any k+1 problems.

How many ways to assign scores do you have? Find this number modulo the given prime M.

Constraints

2 \leq N \leq 5000

9 \times 10^8 < M < 10^9

M is a prime.

All input values are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of ways to assign scores to the problems, modulo M.

Sample Input 1

2 998244353

Sample Output 1

3

The possible assignments are (1, 1), (1, 2), (2, 2).

Sample Input 2

3 998244353

Sample Output 2

7

The possible assignments are (1, 1, 1), (1, 2, 2), (1, 3, 3), (2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3).

Sample Input 3

6 966666661

Sample Output 3

66

Sample Input 4

96 925309799

Sample Output 4

83779

Solution in C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

//set many funcs template
//Ver.20190820
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<stdbool.h>
#include<time.h>
#include<assert.h>
#define inf 1072114514
#define llinf 4154118101919364364
#define mod 1000000007
#define pi 3.1415926535897932384
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target ("sse4")

int max(int a,int b){if(a>b){return a;}return b;}
int min(int a,int b){if(a<b){return a;}return b;}
int zt(int a,int b){return max(a,b)-min(a,b);}
int round(int a,int b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
int ceil(int a,int b){if(a%b==0){return a/b;}return (a/b)+1;}
int gcd(int a,int b){int c;while(b!=0){c=a%b;a=b;b=c;}return a;}
int lcm(int a,int b){int c=gcd(a,b);a/=c;return a*b;}
int nCr(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
int nHr(int a,int b){return nCr(a+b-1,b);}
int fact(int a){int i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
int pow(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
int dsum(int x){int r=0;while(x){r+=(x%10);x/=10;}return r;}
int dsumb(int x,int b){int r=0;while(x){r+=(x%b);x/=b;}return r;}
int sankaku(int x){return ((1+x)*x)/2;}
void swap(int *a,int *b){int c;c=(*a);(*a)=(*b);(*b)=c;}
long long llmax(long long a,long long b){if(a>b){return a;}return b;}
long long llmin(long long a,long long b){if(a<b){return a;}return b;}
long long llzt(long long a,long long b){return llmax(a,b)-llmin(a,b);}
long long llround(long long a,long long b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
long long llceil(long long a,long long b){if(a%b==0){return a/b;}return (a/b)+1;}
long long llgcd(long long a,long long b){long long c;while(b!=0){c=a%b;a=b;b=c;}return a;}
long long lllcm(long long a,long long b){long long c=llgcd(a,b);a/=c;return a*b;}
long long llnCr(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
long long llnHr(long long a,long long b){return llnCr(a+b-1,b);}
long long llfact(long long a){long long i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
long long llpow(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
long long lldsum(long long x){long long r=0;while(x){r+=(x%10);x/=10;}return r;}
long long lldsumb(long long x,long long b){long long r=0;while(x){r+=(x%b);x/=b;}return r;}
long long llsankaku(long long x){return ((1+x)*x)/2;}
void llswap(long long *a,long long *b){long long c;c=(*a);(*a)=(*b);(*b)=c;}
double dbmax(double a,double b){if(a>b){return a;}return b;}
double dbmin(double a,double b){if(a<b){return a;}return b;}
double dbzt(double a,double b){return dbmax(a,b)-dbmin(a,b);}
void dbswap(double *a,double *b){double c;c=(*a);(*a)=(*b);(*b)=c;}
void chswap(char *a,char *b){char c;c=(*a);(*a)=(*b);(*b)=c;}
int sortfncsj(const void *a,const void *b){if(*(int *)a>*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int sortfnckj(const void *a,const void *b){if(*(int *)a<*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int llsortfncsj(const void *a,const void *b){if(*(long long *)a>*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int llsortfnckj(const void *a,const void *b){if(*(long long *)a<*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int dbsortfncsj(const void *a,const void *b){if(*(double *)a>*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int dbsortfnckj(const void *a,const void *b){if(*(double *)a<*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int strsortfncsj(const void *a,const void *b){return strcmp((char *)a,(char *)b);}
int strsortfnckj(const void *a,const void *b){return strcmp((char *)b,(char *)a);}
int chsortfncsj(const void *a,const void *b){if(*(char *)a>*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}
int chsortfnckj(const void *a,const void *b){if(*(char *)a<*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}

void shuffledget(int x[],int n){
    int i,b[524288],p,c;
    for(i=0;i<n;i++){
        b[i]=i;
    }
    for(i=n;i>=1;i--){
        p=rand()%i;
        c=b[i-1];b[i-1]=b[p];b[p]=c;
    }
    for(i=0;i<n;i++){
        scanf("%d",&x[b[i]]);
    }
}

int dx4[4]={1,-1,0,0};
int dy4[4]={0,0,1,-1};
int dx8[8]={-1,-1,-1,0,0,1,1,1};
int dy8[8]={-1,0,1,-1,1,-1,0,1};

int search(int x,int a[],int n){
    int st=0,fi=n-1,te;
    while(st<=fi){
        te=(st+fi)/2;
        if(a[te]<x){st=te+1;}else{fi=te-1;}
    }
    return st;
}

void prarr(int arr[],int n){
  int i;
  for(i=0;i<n;i++){
    if(i){printf(" ");}
    printf("%d",arr[i]);
  }
  printf("\n");
  return;
}

void getperm(int a[],int n){
  int i,p;
  for(i=0;i<n;i++){
    a[i]=i;
  }
  for(i=n-1;i>=1;i--){
    p=rand()%(i+1);
    swap(&a[p],&a[i]);
  }
}

typedef struct{
int val;
int node;
}sd;

int sdsortfnc(const void *a,const void *b){
if(((sd*)a)->val < ((sd*)b)->val){return -1;}
if(((sd*)a)->val > ((sd*)b)->val){return 1;}
return 0;
}

void coordinate_comp(int a[],int n){
  int i,c=0;
  sd dat[524288];
  for(i=0;i<n;i++){
    dat[i].val=a[i];
    dat[i].node=i;
  }
  qsort(dat,n,sizeof(dat[0]),sdsortfnc);
  a[dat[0].node]=c;
  for(i=1;i<n;i++){
    if(dat[i-1].val!=dat[i].val){c++;}
    a[dat[i].node]=c;
  }
}

int main(void){
  long long i,j,n,m,k,a,b,c,h,w,r=0,l,t,lim,os;
  long long **dp=malloc(sizeof(long long*)*5555);
  long long **ndp=malloc(sizeof(long long*)*5555);
  long long **dx=malloc(sizeof(long long*)*5555);
  for(i=0;i<5555;i++){
    dp[i]=malloc(sizeof(long long)*5555);
    ndp[i]=malloc(sizeof(long long)*5555);
    dx[i]=malloc(sizeof(long long)*5555);
    for(j=0;j<5555;j++){
      dp[i][j]=0;
      ndp[i][j]=0;
      dx[i][j]=0;
    }
  }
  long long kr,gr;
  scanf("%lld%lld",&n,&m);
  for(i=1;i<=n;i++){
    dp[n-i][i]=1;
  }
  //for(j=0;j<4;j++){
  //  for(k=0;k<4;k++){
  //    fprintf(stderr,"[%lld]",dp[j][k]);
  //  }fprintf(stderr,"\n");
  //}fprintf(stderr,"\n");
  t=n/2;
  lim=n;
  for(i=1;i<=t;i++){
    for(j=0;j<=lim;j++){
      for(k=n;k>=0;k--){
        a=j;b=k-j;os=0;
        if(b<0){os=-b;a+=b;b=0;}
        if(a>=0){
          dx[a][b]+=dp[j][k];
          ndp[a][b]+=os*dp[j][k];
        }
      }
    }
    lim=n/i;
    kr=0;gr=0;
    for(j=lim;j>=0;j--){
      for(k=0;k<=n;k++){
        dx[j][k]%=m;
        ndp[j][k]+=dx[j][k];
        ndp[j][k]%=m;
        if(j!=0){
          ndp[j-1][k+1]+=ndp[j][k];
          dx[j-1][k+1]+=dx[j][k];
        }
        dp[j][k]=ndp[j][k];
        if(i==t && k!=0){
          kr+=dp[j][k];kr%=m;
          if(j==0){gr+=dp[j][k];gr%=m;}
        }
        ndp[j][k]=0;
        dx[j][k]=0;
      }
    }
    //for(j=0;j<4;j++){
    //  for(k=0;k<4;k++){
    //    fprintf(stderr,"[%lld]",dp[j][k]);
    //  }fprintf(stderr,"\n");
    //}fprintf(stderr,"\n");
  }
  if(n%2==1){printf("%lld\n",kr);}
  else{printf("%lld\n",gr);}
  return 0;
}