#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 998244353; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acos(-1.0); ll mod_pow(ll x, ll n, ll m=mod) { ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } ll gcd(ll a, ll b) { if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } //x,yがax+by=gcd(a,b)の解になる ll extgcd(ll a, ll b, ll& x, ll& y) { ll d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else { x = 1; y = 0; } return d; } //aのmod mでの逆元を求める ll mod_inverse(ll a, ll m) { ll x, y; extgcd(a, m, x, y); return (m + x % m) % m; } int cnte[2001]; vector

ps[2001]; void init() { rep1(n, 2000) { rep1(j, n - 1) { if (gcd(n, j) == 0)cnte[n]++; } int cop = n; for (int j = 2; j <= n; j++) { if (cop % j == 0) { int cnt = 0; while (cop % j == 0) { cop /= j; cnt++; } ps[n].push_back({ j,cnt }); } } } } ll num(ll a, ll n) { if (n == 0)return 1; else if (n >= 3) { return 16; } else if (n == 1)return min(a, (ll)16); else { if (a == 2)return 4; else return 16; } } ll rem(ll r0, ll m0, ll r1, ll m1) { ll x = r0; ll y = (r1 - r0) * mod_inverse(m0, m1); y = (y % m1 + m1) % m1; return x + y * m0; } ll calc(ll a, ll n, ll m) { if (n == 0)return 1; if (m == 1)return 0; ll r = 0, p = 1; rep(j, ps[m].size()) { int sp = ps[m][j].first; int np = 1; rep(i, ps[m][j].second) { np *= sp; } int nm = np*(sp-1)/sp; //a^^n mod np int cnt = 0; int cop = a; while (cop % sp == 0) { cnt++; cop /= sp; } ll r1, r2; { //cop ll v = calc(a, n - 1, nm); r1 = 1; rep(i, v)r1 = r1 * cop % np; } { //sp ll cc = num(a, n - 1); if (cc * cnt >= ps[m][j].second)r2 = 0; else { r2 = 1; rep(aa, cc* cnt)r2 *= sp; } } ll nr = r1 * r2 % np; r = rem(r, p, nr, np); p *= np; } return r; } void solve() { ll a, n, m; cin >> a >> n >> m; if (m == 1) { cout << 0 << "\n"; return; } if (a == 1) { cout << 1%m << "\n"; return; } cout << calc(a, n, m) << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(10); //init_f(); init(); //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }