#include #include #include using namespace atcoder; using mint = modint998244353; using namespace std; #define rep(i,n) for (int i = 0; i < (n); ++i) #define Inf32 1000000001 #define Inf64 1000000000000000001 long long N,P; bool check(long long g){ vector f(P,false); long long tg = g; g = 1; rep(i,P-1){ if(f[g])return false; f[g] = true; g *= tg; g %= P; } return true; } long long frac[200005]; long long ifrac[200005]; long long get(long long n,long long r){ if(n>N>>P; long long g; for(long long i=1;true;i=(i+(P/2))%P){ if(check(i)){ g = i; break; } } vector pos(P); pos[1] = 0; vector t(1,1); rep(i,P-2){ t.push_back(t.back()*g%P); pos[t.back()] = t.size()-1; } vector bs; while(N!=0){ bs.push_back(N%P); N /= P; } reverse(bs.begin(),bs.end()); frac[0] = 1; rep(i,P){ frac[i+1] = frac[i] * (i+1); frac[i+1] %= P; } rep(i,P)ifrac[i] = inv_mod(frac[i],P); vector dp(2,vector(P-1,0)); dp[0][0] = 1; rep(i,bs.size()){ vector ndp(2,vector(P-1,0)); { vector x = dp[1]; vector y(P); rep(j,P){ int tt = get(bs[i],j); if(tt!=0)y[pos[tt]] ++; } x = convolution(x,y); while(x.size()>=P){ mint tt = x.back(); x.pop_back(); x[x.size()%(P-1)] += tt; } ndp[1] = x; } { vector x = dp[0]; vector y(P); rep(j,bs[i]){ int tt = get(bs[i],j); if(tt!=0)y[pos[tt]] ++; } x = convolution(x,y); while(x.size()>=P){ mint tt = x.back(); x.pop_back(); x[x.size()%(P-1)] += tt; } rep(j,x.size())ndp[1][j] += x[j]; } { vector x = dp[0]; vector y(P); rep(j,bs[i]+1){ if(j=P){ mint tt = x.back(); x.pop_back(); x[x.size()%(P-1)] += tt; } rep(j,x.size())ndp[0][j] += x[j]; } swap(dp,ndp); } mint ans = 0; rep(i,2){ rep(j,P-1){ mint tt = t[j]; tt *= dp[i][j]; ans += tt; } } cout<