#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #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; //constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #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; template void chmin(T& a, T b) { a = min(a, b); } template void chmax(T& a, T b) { a = max(a, b); } template void cinarray(vector& v) { rep(i, v.size())cin >> v[i]; } template void coutarray(vector& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; //if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } //mod should be <2^31 struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.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 -= (int)mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)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)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } 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]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } using ld = long double; //typedef long double ld; typedef pair LDP; const ld eps = 1e-10; const ld pi = acosl(-1.0); template void addv(vector& v, int loc, T val) { if (loc >= v.size())v.resize(loc + 1, 0); v[loc] += val; } /*const int mn = 2000005; bool isp[mn]; vector ps; void init() { fill(isp + 2, isp + mn, true); for (int i = 2; i < mn; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < mn; j += i) { isp[j] = false; } } }*/ //[,val) template auto prev_itr(set& st, T val) { auto res = st.lower_bound(val); if (res == st.begin())return st.end(); res--; return res; } //[val,) template auto next_itr(set& st, T val) { auto res = st.lower_bound(val); return res; } using mP = pair; mP operator+(mP a, mP b) { return { a.first + b.first,a.second + b.second }; } mP operator+=(mP& a, mP b) { a = a + b; return a; } mP operator-(mP a, mP b) { return { a.first - b.first,a.second - b.second }; } mP operator-=(mP& a, mP b) { a = a - b; return a; } LP operator+(LP a, LP b) { return { a.first + b.first,a.second + b.second }; } LP operator+=(LP& a, LP b) { a = a + b; return a; } LP operator-(LP a, LP b) { return { a.first - b.first,a.second - b.second }; } LP operator-=(LP& a, LP b) { a = a - b; return a; } mt19937 mt(time(0)); const string drul = "DRUL"; string senw = "SENW"; //DRUL,or SENW int dx[4] = { 1,0,-1,0 }; int dy[4] = { 0,1,0,-1 }; //----------------------------------------- ll calc(ll n) { ll sum = 0; rep1(i, n - 1) { ll pro = 1; rep1(j, i) { pro *= n - j + 1; pro *= n - j + 1; } Rep1(j, i + 1, n) { pro *= j; pro *= j; } sum += pro; } ll pro = 1; rep1(i, n)pro *= i; sum /= pro; sum /= pro; return sum; } void expr() { rep1(n, 20) { cout << n << " " << calc(n) << "\n"; } } //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; } ll f(ll n, ll p) { ll res = 0; while (n) { res += n / p; n /= p; } return res; } //mod p^q ll calc(ll le, ll ri, ll p, ll q) { ll pp = 1; rep(i, q)pp *= p; //ll res = 0; ll curv = 1, curc = 0; auto calc_val = [&]() { assert(curv < pp); ll res = curv; for (ll i = 0; i < curc; i++) { res = res * p % pp; if (res == 0)break; } return res; }; //binomial[2*le,le] curc = f(2 * le, p) - 2 * f(le, p); rep(i, pp) { if (i % p == 0)continue; ll cnt = 0; ll s = 2 * le; while (i <= s) { cnt += (s - i) / pp + 1; s /= p; } s = le; while (i <= s) { cnt -= (s - i) / pp + 1; cnt -= (s - i) / pp + 1; s /= p; } ll adv = i; if (cnt < 0) { adv = mod_inverse(i, pp); cnt *= -1; } curv = curv * mod_pow(adv, cnt, pp) % pp; } /*rep(i, pp) { if (i == 0)continue; ll adv = i; while (adv % p == 0)adv /= p; adv %= pp; ll cnt = 0; if (2 * le >= i) { cnt += (2*le - i) / pp + 1; } if (le >= i) { cnt -= (le - i) / pp + 1; cnt -= (le - i) / pp + 1; } if (cnt < 0) { adv = mod_inverse(adv, pp); cnt *= -1; } curv = curv * mod_pow(adv, cnt, pp) % pp; }*/ auto add = [&](ll x) { while (x % p == 0) { x /= p; curc++; } x %= pp; assert(x% p); assert(x < pp); curv = curv * x % pp; }; auto add_b = [&](ll x) { while (x % p == 0) { x /= p; curc--; } x %= pp; x = mod_inverse(x, pp); assert(x% p); assert(x < pp); curv = curv * x % pp; }; assert(curv < pp); //if(p==5)cout << "! " << curv << "\n"; ll res = calc_val(); for (ll i = le + 1; i <= ri; i++) { //cout << res <<" "<> l >> r >> m; vector ps; for (ll i = 2; i <= m; i++) { if (m % i == 0) { int cnt = 0; while (m % i == 0) { m /= i; cnt++; } ps.push_back({ i,cnt }); } } ll ans = 0; ll ansm = 1; rep(i, ps.size()) { ll p = ps[i].first; ll q = ps[i].second; ll pp = 1; rep(i, q)pp *= p; ll val = calc(l, r, p, q); //cout << "?? " << p << " " << q << " " << val << "\n"; //= val mod pp while (ans % pp != val) { ans += ansm; } ansm *= pp; //cout << ans << " " << ansm << "\n"; } ans -= 2 * (r - l + 1); while (ans < 0)ans += ansm; cout << ans << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(10); //init_f(); //init(); //expr(); //while(true) //int t; cin >> t; rep(i, t) solve(); return 0; }