#define _USE_MATH_DEFINES #include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 998244353; // constexpr int MOD = 1000000007; constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1}; constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}; constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; template struct MInt { unsigned int v; MInt() : v(0) {} MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {} static constexpr int get_mod() { return M; } static void set_mod(const int divisor) { assert(divisor == M); } static void init(const int x = 10000000) { inv(x, true); fact(x); fact_inv(x); } static MInt inv(const int n, const bool init = false) { // assert(0 <= n && n < M && std::__gcd(n, M) == 1); static std::vector inverse{0, 1}; const int prev = inverse.size(); if (n < prev) { return inverse[n]; } else if (init) { // "n!" and "M" must be disjoint. inverse.resize(n + 1); for (int i = prev; i <= n; ++i) { inverse[i] = -inverse[M % i] * (M / i); } return inverse[n]; } int u = 1, v = 0; for (unsigned int a = n, b = M; b;) { const unsigned int q = a / b; std::swap(a -= q * b, b); std::swap(u -= q * v, v); } return u; } static MInt fact(const int n) { static std::vector factorial{1}; const int prev = factorial.size(); if (n >= prev) { factorial.resize(n + 1); for (int i = prev; i <= n; ++i) { factorial[i] = factorial[i - 1] * i; } } return factorial[n]; } static MInt fact_inv(const int n) { static std::vector f_inv{1}; const int prev = f_inv.size(); if (n >= prev) { f_inv.resize(n + 1); f_inv[n] = inv(fact(n).v); for (int i = n; i > prev; --i) { f_inv[i - 1] = f_inv[i] * i; } } return f_inv[n]; } static MInt nCk(const int n, const int k) { if (n < 0 || n < k || k < 0) return 0; return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) : fact_inv(n - k) * fact_inv(k)); } static MInt nPk(const int n, const int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); } static MInt nHk(const int n, const int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); } static MInt large_nCk(long long n, const int k) { if (n < 0 || n < k || k < 0) return 0; inv(k, true); MInt res = 1; for (int i = 1; i <= k; ++i) { res *= inv(i) * n--; } return res; } MInt pow(long long exponent) const { MInt res = 1, tmp = *this; for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= tmp; tmp *= tmp; } return res; } MInt& operator+=(const MInt& x) { if (static_cast(v += x.v) >= M) v -= M; return *this; } MInt& operator-=(const MInt& x) { if (static_cast(v += M - x.v) >= M) v -= M; return *this; } MInt& operator*=(const MInt& x) { v = static_cast(v) * x.v % M; return *this; } MInt& operator/=(const MInt& x) { return *this *= inv(x.v); } bool operator==(const MInt& x) const { return v == x.v; } bool operator!=(const MInt& x) const { return v != x.v; } bool operator<(const MInt& x) const { return v < x.v; } bool operator<=(const MInt& x) const { return v <= x.v; } bool operator>(const MInt& x) const { return v > x.v; } bool operator>=(const MInt& x) const { return v >= x.v; } MInt& operator++() { if (static_cast(++v) == M) v = 0; return *this; } MInt operator++(int) { const MInt res = *this; ++*this; return res; } MInt& operator--() { v = (v == 0 ? M - 1 : v - 1); return *this; } MInt operator--(int) { const MInt res = *this; --*this; return res; } MInt operator+() const { return *this; } MInt operator-() const { return MInt(v ? M - v : 0); } MInt operator+(const MInt& x) const { return MInt(*this) += x; } MInt operator-(const MInt& x) const { return MInt(*this) -= x; } MInt operator*(const MInt& x) const { return MInt(*this) *= x; } MInt operator/(const MInt& x) const { return MInt(*this) /= x; } friend std::ostream& operator<<(std::ostream& os, const MInt& x) { return os << x.v; } friend std::istream& operator>>(std::istream& is, MInt& x) { long long v; is >> v; x = MInt(v); return is; } }; using ModInt = MInt; struct Mo { explicit Mo(const std::vector& ls, const std::vector& rs) : n(ls.size()), ptr(0), nl(0), nr(0), ls(ls), rs(rs) { const int width = std::round(std::sqrt(n)); order.resize(n); std::iota(order.begin(), order.end(), 0); std::sort(order.begin(), order.end(), [&ls, &rs, width](const int a, const int b) -> bool { if (ls[a] / width != ls[b] / width) return ls[a] < ls[b]; return (ls[a] / width) & 1 ? rs[a] < rs[b] : rs[a] > rs[b]; }); } int process() { if (ptr == n) return -1; const int id = order[ptr++]; while (ls[id] < nl) add(--nl); while (nr < rs[id]) add(nr++); while (nl < ls[id]) del(nl++); while (rs[id] < nr) del(--nr); return id; } void add(const int idx) const; void del(const int idx) const; private: const int n; int ptr, nl, nr; std::vector ls, rs, order; }; int len; ModInt v = 0; vector b; vector p2; void Mo::add(const int idx) const { if (idx + 1 == nr) { v += p2[nr - nl - 1] * b[idx]; } else { v = v * 2 + b[idx]; if (nl + 1 < nr) v -= b[nl + 1]; } // REP(i, b.size()) cout << b[i] << " \n"[i + 1 == b.size()]; // cout << nl << ' ' << nr << ": " << v << '\n'; } void Mo::del(const int idx) const { if (idx == nr) { v -= p2[nr - nl] * b[idx]; } else { v -= b[idx]; if (nl < nr) v = (v - b[nl]) / 2 + b[nl]; } // REP(i, b.size()) cout << b[i] << " \n"[i + 1 == b.size()]; // cout << nl << ' ' << nr << ": " << v << '\n'; } int main() { int n, q; cin >> n >> q; vector a(n), l(q), r(q); REP(i, n) cin >> a[i]; REP(i, q) cin >> l[i] >> r[i], --l[i], --r[i]; p2.assign(n, 1); FOR(i, 2, n) p2[i] = p2[i - 1] * 2; vector> queries(n); REP(i, q) queries[r[i]].emplace_back(i); vector ans(q, 0); for (int i = n - 1; i >= 0;) { int j = i; while (j > 0 && a[j - 1] < a[j]) --j; vector ls, rs, ids; FOR(k, j, i + 1) { for (const int id : queries[k]) { ls.emplace_back(max(l[id], j) - j); rs.emplace_back(r[id] - j + 1); ids.emplace_back(id); } } if (!ls.empty()) { len = i - j + 1; v = 0; b.resize(len); copy(next(a.begin(), j), next(a.begin(), i + 1), b.begin()); Mo mo(ls, rs); while (true) { const int id = mo.process(); if (id == -1) break; ans[ids[id]] = v; } } // for (const int id : queries[i]) { // for (int fib_index = 0, p = max(j, l[id]); p <= i; ++fib_index, ++p) { // ans[id] += fib[fib_index] * a[p]; // } // } i = j - 1; } REP(i, q) cout << ans[i] << '\n'; // REP(i, q) { // vector b(r[i] - l[i] + 1); // copy(next(a.begin(), l[i]), next(a.begin(), r[i] + 1), b.begin()); // while (b.size() > 1) { // const int x = distance(b.begin(), max_element(ALL(b))); // REP(j, x) b[j] += b[x]; // b.erase(next(b.begin(), x)); // } // assert(ans[i] == b.front()); // } return 0; }