#include #pragma GCC optimize("Ofast") using namespace std; using std::cout; using std::cin; using std::endl; using ll=long long; using ld=long double; ll ILL=2167167167167167167; const int INF=2100000000; const ll mod=998244353; #define rep(i,a,b) for (ll i=a;i using _pq = priority_queue, greater>; template ll LB(vector &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} template ll UB(vector &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();} template bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;} template bool chmax(T &a,const T &b){if(a void So(vector &v) {sort(v.begin(),v.end());} template void Sore(vector &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});} void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";} template void vec_out(vector &p){for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout< T min(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;} template T max(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;} template T sum(vector &a){assert(!a.empty());T ans=a[0]-a[0];for(auto &x:a) ans+=x;return ans;} //a*x+b*y=gcd(a,b)となるx,yにする 返り値gcd(a,b) ll Euclid(ll a,ll b,ll &x,ll &y){ if(b==0){ x=1,y=0; return a; } ll d=Euclid(b,a%b,y,x); y-=a/b*x; return d; } // val1=(a,p) val2=(b,q) // return (c,r) // c: c%p==a && c%q==b // r: r=lcm(a,b) // need: a%gcd(p,q)==b%gcd(p,q) // use: Euclid std::pair ctr_sub(std::pair val1,std::pair val2){ long long a,b,p,q; long long X,Y,G,ans_val,ans_mod; tie(a,p)=val1; tie(b,q)=val2; G=Euclid(p,q,X,Y); if((b-a)%G!=0) return {-1,-1}; ans_mod=p*(q/G); ans_val=(p*((X*((b-a)/G))%q))%ans_mod+a; return {(ans_val%ans_mod+ans_mod)%ans_mod,ans_mod}; } // return val=p(N) // a=p[0].first^p[0].second * ... *p[N-1].first^p[N-1].second // for all i: p[i].first is prime number // O(sqrt(val)) std::vector> Prime_factorization(long long val){ assert(val>=1); if(val==1){ return {}; } int ind=0; std::vector> ans; for(long long i=2;i*i<=val;i++){ if(val%i!=0) continue; ans.push_back({i,0}); while(val%i==0){ ans[ind].second++; val/=i; } ind++; } if(val!=1) ans.push_back({val,1}); return ans; } ll jyo(ll x,ll y,ll z){ ll H=y; //ここから ll a=1,b=(x%z+z)%z,c=1; while(H>0){ a*=2; if(H%a!=0){ H-=a/2; c*=b; c%=z; } b*=b; b%=z; } //ここまで return c; } //最大公約数 long long Gcd(long long a,long long b){ if(b==0) return a; else return Gcd(b,a%b); } //最小公倍数 long long Lcm(long long a,long long b){ return (a/Gcd(a,b))*b; } //カーマイケル数の出力 long long carmichael(long long a){ long long ans=1,A=1; //2を素因数に持つときだけ場合わけ while(a%2==0) A*=2,a/=2; if(A==4) ans=2; else if(A>4) ans=A/4; A=a; for(long long k=3;k*k<=a;k++){ //for(auto k:div){ //配列divをsqrt(a)以下の素数を全列挙するやつにする if(A%k==0){ long long B=k-1; A/=k; while(A%k==0) A/=k,B*=k; ans=Lcm(ans,B); } } if(A!=1) ans=Lcm(ans,A-1); return ans; } void solve(); // oddloop int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t=1; //cin>>t; rep(i,0,t) solve(); } void solve(){ auto f=[&](auto self,int p,int _mod,ll n)->ll{ if(n<=1) return 1; ll ans=1,Y=n/_mod; if(Y%2==1&&p!=2) ans=_mod-1; rep(R,Y*_mod+1,n+1){ ll tmp=R; while(tmp%p==0) tmp/=p; tmp%=_mod; ans=(ans*tmp)%_mod; } return (ans*self(self,p,_mod,Y*(_mod/p)))%_mod; }; auto g=[&](auto self,int p,ll n)->ll{ if(n==0) return 0; return n/p+self(self,p,n/p); }; auto h=[&](ll x,int p,int _mod)->pair{ pair ans={0,0}; while(x%p==0) x/=p,ans.second++; ans.first=x%_mod; return ans; }; ll L,R,M; cin>>L>>R>>M; if(M==1){ cout<<"0\n"; return; } auto pri=Prime_factorization(M); int S=pri.size(); vector Q(S,1); vector C(S,1); vector sum(S); vector mul(S),cou(S); rep(j,0,S){ rep(k,0,pri[j].second) Q[j]*=pri[j].first; cou[j]=g(g,pri[j].first,2*L)-2*g(g,pri[j].first,L); C[j]=carmichael(Q[j]); mul[j]=f(f,pri[j].first,Q[j],L*2); mul[j]=(mul[j]*jyo(f(f,pri[j].first,Q[j],L),C[j]-2,Q[j]))%Q[j]; } rep(i,L,R+1){ rep(j,0,S){ ll tmp=mul[j]; rep(k,0,min(cou[j],pri[j].second)) tmp=(tmp*pri[j].first)%Q[j]; //if(cou[j] ans={0,1}; rep(j,0,S){ ans=ctr_sub(ans,{sum[j],Q[j]}); } cout<