#include #include #define rep(i,b) for(int i=0;i=0;i--) #define rep1(i,b) for(int i=1;i=x;i--) #define fore(i,a) for(auto i:a) #define fore1(i,a) for(auto &i:a) #define rng(x) (x).begin(), (x).end() #define rrng(x) (x).rbegin(), (x).rend() #define sz(x) ((int)(x).size()) #define pb push_back #define fi first #define se second #define pcnt __builtin_popcountll using namespace std; using namespace atcoder; using ll = long long; using ld = long double; template using mpq = priority_queue, greater>; template bool chmax(T &a, const T &b) { if (a bool chmin(T &a, const T &b) { if (b ll sumv(const vector&a){ll res(0);for(auto&&x:a)res+=x;return res;} bool yn(bool a) { if(a) {cout << "Yes" << endl; return true;} else {cout << "No" << endl; return false;}} #define dame { cout << "No" << endl; return;} #define dame1 { cout << -1 << endl; return;} #define cout2(x,y) cout << x << " " << y << endl; #define coutp(p) cout << p.fi << " " << p.se << endl; #define out cout << ans << endl; #define outd cout << fixed << setprecision(20) << ans << endl; #define outm cout << ans.val() << endl; #define outv fore(yans , ans) cout << yans << "\n"; #define outdv fore(yans , ans) cout << yans.val() << "\n"; #define coutv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;} #define coutv2(v) fore(vy , v) cout << vy << "\n"; #define coutvm(v) {fore(vy , v) {cout << vy.val() << " ";} cout << endl;} #define coutvm2(v) fore(vy , v) cout << vy.val() << "\n"; using pll = pair;using pil = pair;using pli = pair;using pii = pair;using pdd = pair; using tp = tuple; using vi = vector;using vd = vector;using vl = vector;using vs = vector;using vb = vector; using vpii = vector;using vpli = vector;using vpll = vector;using vpil = vector; using vvi = vector>;using vvl = vector>;using vvs = vector>;using vvb = vector>; using vvpii = vector>;using vvpli = vector>;using vvpll = vector;using vvpil = vector; // using mint = modint998244353; //using mint = modint1000000007; using mint = dynamic_modint<0>; using vm = vector; using vvm = vector>; vector dx={1,0,-1,0,1,1,-1,-1},dy={0,1,0,-1,1,-1,1,-1}; ll gcd(ll a, ll b) { return a?gcd(b%a,a):b;} ll lcm(ll a, ll b) { return a/gcd(a,b)*b;} #define yes {cout <<"Yes"< f, primes; Sieve(int n=1):n(n), f(n+1) { //初期化、f[x] = (xの最も小さい素因数) f[0] = f[1] = -1; for (ll i = 2; i <= n; ++i) { if (f[i]) continue; primes.push_back(i); f[i] = i; for (ll j = i*i; j <= n; j += i) { if (!f[j]) f[j] = i; } } } bool isPrime(int x) { return f[x] == x;} //素数判定 vector factorList(int x) {//素因数分解、xの素因数を小さいものから個数分列挙 vector res; while (x != 1) { res.push_back(f[x]); x /= f[x]; } return res; } vector factor(int x) {//素因数分解その2、xの素因数を小さいものから(素因数、個数)の形で列挙 vector fl = factorList(x); if (fl.size() == 0) return {}; vector res(1, pii(fl[0], 0)); for (int p : fl) { if (res.back().first == p) { res.back().second++; } else { res.emplace_back(p, 1); } } return res; } vector factor(ll x) {//素因数分解その2-2、xがllの場合 vector res; for (int p : primes) { int y = 0; while (x%p == 0) x /= p, ++y; if (y != 0) res.emplace_back(p,y); } if (x != 1) res.emplace_back(x,1); return res; } } sieve(1e6); // .primes : n以下の素数を小さい順で格納しているベクトル。 // .isPrime(int x) : xの素数判定。boolで返す // .factorList(int x) : xの素因数分解。xの素因数を小さいものから個数分列挙。vectorで返す。 // .factor(int x) : 素因数分解その2、xの素因数を小さいものからpair{素因数、個数}の形で列挙。vectorで返す。xはllでもok。 // 宣言方法 : n=1e6(デフォルト)で初期化している。 // 注意点 : factorList、factorは呼び出し毎に約数個分の計算時間がかかってしまうため、何度も呼び出すときは予め別の配列に格納しておくこと。 void solve(){ ll l,r;int m; cin>>l>>r>>m; mint::set_mod(m); vpii p = sieve.factor(m); unordered_map mp; fore(y , p) mp[y.fi] = 0; auto check = [&](ll n)->mint{ mint ret = 1; fore(y , p){ ll cnt = 0; ll now = y.fi; ll k = n; while(now <= k){ cnt -= (k/now)*2; if (now >= LLONG_MAX/y.fi) break; now *= y.fi; } now = y.fi; k = n*2; while(now <= k){ cnt += (k/now); if (now >= LLONG_MAX/y.fi) break; now *= y.fi; } ret *= mint(y.fi).pow(cnt); } return ret; }; vm v(m); v[0] = 1; rep1(i,m){ vpii tmp = sieve.factor(i); v[i] = v[i-1]; fore(y , tmp){ if (mp.count(y.fi)) continue; v[i] *= mint(y.fi).pow(y.se); } } mint ans = 0; for(ll i=l;i<=r;i++){ mint tmp = check(i); ll t = i*2; tmp *= mint(v[m-1]).pow(t/m) * v[t%m]; t = i; tmp /= mint(v[m-1]).pow(t/m) * v[t%m]; tmp /= mint(v[m-1]).pow(t/m) * v[t%m]; ans += tmp; } ans -= mint(r-l+1)*2; outm; return; } int main(){ ios::sync_with_stdio(false); cin.tie(0); int t = 1; //cin>>t; rep(i,t){ solve(); } return 0; }