#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; // using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } #ifndef LIBRA_OTHER_INT128_H_ #define LIBRA_OTHER_INT128_H_ #include #include constexpr unsigned __int128 toUInt128(const char *s) { unsigned __int128 x = 0; for (; *s; ++s) x = x * 10 + (*s - '0'); return x; } constexpr __int128 toInt128(const char *s) { if (*s == '-') return -toInt128(s + 1); __int128 x = 0; for (; *s; ++s) x = x * 10 + (*s - '0'); return x; } unsigned __int128 inUInt128() { static char buf[41]; scanf("%s", buf); return toUInt128(buf); } __int128 inInt128() { static char buf[41]; scanf("%s", buf); return toInt128(buf); } void out(unsigned __int128 x) { static char buf[41]; int len = 0; do { buf[len++] = '0' + static_cast(x % 10); } while (x /= 10); for (int i = len; --i >= 0; ) putchar(buf[i]); } void out(__int128 x) { if (x < 0) { putchar('-'); out(-static_cast(x)); } else { out(static_cast(x)); } } std::ostream &operator<<(std::ostream &os, unsigned __int128 x) { static char buf[41]; int len = 0; do { buf[len++] = '0' + static_cast(x % 10); } while (x /= 10); for (int i = len; --i >= 0; ) os << buf[i]; return os; } std::ostream &operator<<(std::ostream &os, __int128 x) { if (x < 0) { os << '-' << -static_cast(x); } else { os << static_cast(x); } return os; } #endif // LIBRA_OTHER_INT128_H_ // y^f(0) x y^(f(1)-f(0)) x y^(f(2)-f(1)) x ... x y^(f(n)-f(n-1)) // where f(i) = floor((a i + b) / m) // S: (unsigned or signed) integer // (a n + b) and (m + a) does not overflow // T: monoid with pow // e: identity template T pathUnder(S m, S a, S b, S n, T e, T x, T y) { assert(m >= 1); assert(a >= 0); assert(b >= 0); assert(n >= 0); S c = (a * n + b) / m; T pre = e, suf = e; for (; ; ) { const S p = a / m; a %= m; x = x * y.pow(p); const S q = b / m; b %= m; pre = pre * y.pow(q); c -= (p * n + q); if (c == 0) return pre * x.pow(n) * suf; const S d = (m * c - b - 1) / a + 1; suf = y * x.pow(n - d) * suf; b = m - b - 1 + a; swap(m, a); n = c - 1; c = d; swap(x, y); } } using Int = __int128; struct Data { Int val, sz, sum0, sum1; Data() : val(0), sz(0), sum0(0), sum1(0) {} friend Data operator*(const Data &a, const Data &b) { Data c; c.val = a.val + b.val; c.sz = a.sz + b.sz; c.sum0 = a.sum0 + b.sz * a.val + b.sum0; c.sum1 = a.sum1 + b.sz * a.sz * a.val + (b.sz * (b.sz - 1) / 2) * a.val + a.sz * b.sum0 + b.sum1; return c; } Data pow(Int e) const { for (Data a = *this, b; ; a = a * a) { if (e & 1) b = b * a; if (!(e >>= 1)) return b; } } }; // \sum[0<=i