#include #ifdef DEBUG #include #else #define dump(...) #endif /** * @docs input_vector.md */ template std::vector input_vector(int N){ std::vector ret(N); for(int i = 0; i < N; ++i) std::cin >> ret[i]; return ret; } template std::vector> input_vector(int N, int M){ std::vector> ret(N); for(int i = 0; i < N; ++i) ret[i] = input_vector(M); return ret; } /** * @docs input_tuple_vector.md */ template void input_tuple_vector_init(T &val, int N, std::index_sequence){ (void)std::initializer_list{ (void(std::get(val).resize(N)), 0)... }; } template void input_tuple_vector_helper(T &val, int i, std::index_sequence){ (void)std::initializer_list{ (void(std::cin >> std::get(val)[i]), 0)... }; } template auto input_tuple_vector(int N){ std::tuple...> ret; input_tuple_vector_init(ret, N, std::make_index_sequence()); for(int i = 0; i < N; ++i){ input_tuple_vector_helper(ret, i, std::make_index_sequence()); } return ret; } /** * @docs input_tuples.md */ template class InputTuples{ template static void input_tuple_helper(T &val, std::index_sequence){ (void)std::initializer_list{(void(std::cin >> std::get(val)), 0)...}; } struct iter{ using value_type = std::tuple; value_type value; bool get = false; int N; int c = 0; value_type operator*(){ if(get) return value; else{ input_tuple_helper(value, std::make_index_sequence()); return value; } } void operator++(){ ++c; get = false; } bool operator!=(iter &) const { return c < N; } iter(int N): N(N){} }; int N; public: InputTuples(int N): N(N){} iter begin() const {return iter(N);} iter end() const {return iter(N);} }; template auto input_tuples(int N){ return InputTuples(N); } /** * @title modint * @docs mint.md */ template class ModInt{ public: constexpr static uint32_t MOD = M; uint64_t val; constexpr ModInt(): val(0){} constexpr ModInt(int64_t n){ if(n >= M) val = n % M; else if(n < 0) val = n % M + M; else val = n; } inline constexpr auto operator+(const ModInt &a) const {return ModInt(val + a.val);} inline constexpr auto operator-(const ModInt &a) const {return ModInt(val - a.val);} inline constexpr auto operator*(const ModInt &a) const {return ModInt(val * a.val);} inline constexpr auto operator/(const ModInt &a) const {return ModInt(val * a.inv().val);} inline constexpr auto& operator=(const ModInt &a){val = a.val; return *this;} inline constexpr auto& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;} inline constexpr auto& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;} inline constexpr auto& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;} inline constexpr auto& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;} inline constexpr bool operator==(const ModInt &a) const {return val == a.val;} inline constexpr bool operator!=(const ModInt &a) const {return val != a.val;} inline constexpr auto& operator++(){*this += 1; return *this;} inline constexpr auto& operator--(){*this -= 1; return *this;} inline constexpr auto operator++(int){auto t = *this; *this += 1; return t;} inline constexpr auto operator--(int){auto t = *this; *this -= 1; return t;} inline constexpr static ModInt power(int64_t n, int64_t p){ if(p < 0) return power(n, -p).inv(); int64_t ret = 1, e = n % M; for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M; return ret; } inline constexpr static ModInt inv(int64_t a){ int64_t b = M, u = 1, v = 0; while(b){ int64_t t = a / b; a -= t * b; std::swap(a,b); u -= t * v; std::swap(u,v); } u %= M; if(u < 0) u += M; return u; } inline constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);} inline constexpr auto power(int64_t p) const {return power(val, p);} inline constexpr auto inv() const {return inv(val);} friend inline constexpr auto operator-(const ModInt &a){return ModInt(-a.val);} friend inline constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;} friend inline constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;} friend inline constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;} friend inline constexpr auto operator/(int64_t a, const ModInt &b){return ModInt(a) / b;} friend std::istream& operator>>(std::istream &s, ModInt &a){s >> a.val; return s;} friend std::ostream& operator<<(std::ostream &s, const ModInt &a){s << a.val; return s;} template inline static auto div(){ static auto value = inv(N); return value; } explicit operator int32_t() const noexcept {return val;} explicit operator int64_t() const noexcept {return val;} }; /** * @title NumberTheoreticTransform * @docs ntt_convolution.md */ template class NumberTheoreticTransform{ const int MAX_POWER; std::vector BASE, INV_BASE; public: NumberTheoreticTransform(): MAX_POWER(__builtin_ctz(MAX_SIZE)), BASE(MAX_POWER + 1), INV_BASE(MAX_POWER + 1) { static_assert((MAX_SIZE & (MAX_SIZE - 1)) == 0, "MAX_SIZE must be power of 2."); T t = T::power(PRIM_ROOT, (T::MOD-1) >> (MAX_POWER + 2)); T s = t.inv(); for(int i = MAX_POWER - 1; i >= 0; --i){ t *= t; s *= s; BASE[i] = -t; INV_BASE[i] = -s; } } void run_ntt(std::vector &f, bool INVERSE = false){ const int n = f.size(); assert((n & (n-1)) == 0 and n <= MAX_SIZE); // データ数は2の冪乗個 if(INVERSE){ for(int b = 1; b < n; b <<= 1){ T w = 1; for(int j = 0, k = 1; j < n; j += 2 * b, ++k){ for(int i = 0; i < b; ++i){ const auto s = f[i+j]; const auto t = f[i+j+b]; f[i+j] = s + t; f[i+j+b] = (s - t) * w; } w *= INV_BASE[__builtin_ctz(k)]; } } const T t = T::inv(n); for(auto &x : f) x *= t; }else{ for(int b = n >> 1; b; b >>= 1){ T w = 1; for(int j = 0, k = 1; j < n; j += 2 * b, ++k){ for(int i = 0; i < b; ++i){ const auto s = f[i+j]; const auto t = f[i+j+b] * w; f[i+j] = s + t; f[i+j+b] = s - t; } w *= BASE[__builtin_ctz(k)]; } } } } template std::vector run_convolution(std::vector f, std::vector g){ const int m = f.size() + g.size() - 1; int n = 1; while(n < m) n *= 2; std::vector f2(n), g2(n); for(int i = 0; i < (int)f.size(); ++i) f2[i] = f[i]; for(int i = 0; i < (int)g.size(); ++i) g2[i] = g[i]; run_ntt(f2); run_ntt(g2); for(int i = 0; i < n; ++i) f2[i] *= g2[i]; run_ntt(f2, true); return f2; } }; constexpr int mod = 998244353; using mint = ModInt; int main(){ std::cin.tie(0); std::ios::sync_with_stdio(false); int N, Q; std::cin >> N >> Q; auto A = input_vector(N); std::vector ord(N); std::iota(ord.begin(), ord.end(), 0); std::sort(ord.begin(), ord.end(), [&](int i, int j){return A[i] < A[j];}); std::vector c(A); std::sort(c.begin(), c.end()); auto ntt = NumberTheoreticTransform(); std::vector right(N+1); std::vector> left(N+1); right[0] = 1; for(int i = 0; i < N; ++i){ right[i + 1] = A[ord[i]]; } for(int i = 0; i < N; ++i){ right[i + 1] = right[i + 1] * right[i]; } left[N] = {1}; for(int i = 0; i < N; ++i){ left[i] = {A[ord[i]] - 1, 1}; } for(int i = N; i > 0; --i){ left[i - 1] = ntt.run_convolution(left[i - 1], left[i]); if((int)left[i - 1].size() > N + 1) left[i - 1].resize(N + 1); } std::vector> f(N+1); for(int i = 0; i < N + 1; ++i){ f[i] = ntt.run_convolution({right[i]}, left[i]); f[i].resize(N + 1); } for(auto [l, r, p] : input_tuples(Q)){ int ans = 0; for(int i = l; i <= r; ++i){ int j = std::lower_bound(c.begin(), c.end(), i) - c.begin(); ans ^= f[j][p].val; } ans %= mod; std::cout << ans << "\n"; } return 0; }