#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; template struct Mat : array, N> { using M = Mat; void make_identity() { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { (*this)[i][j] = zero(); } } for (int i = 0; i < N; i++) { (*this)[i][i] = one(); } } M& operator+=(const M& rhs) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { (*this)[i][j] = add((*this)[i][j], rhs[i][j]); } } return *this; } M& operator*=(const M& rhs) { static M temp; for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { temp[i][j] = zero(); } } for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { for (int k = 0; k < N; k++) { temp[i][k] = add(temp[i][k], mul((*this)[i][j], rhs[j][k])); } } } *this = temp; return *this; } template void inplace_pow(I k) { assert(k >= 0); static M temp; temp = *this; make_identity(); while (k) { if (k & 1) *this *= temp; k >>= 1; if (k) temp *= temp; } } friend ostream& operator<<(ostream& os, const M& A) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { os << A[i][j] << " \n"[j + 1 == N]; } } return os; } }; // mint mint add(mint x, mint y) { return x + y; } mint zero() { return mint(); } mint mul(mint x, mint y) { return x * y; } mint one() { return mint::raw(1); } using M = Mat; } int main() { ios::sync_with_stdio(false); cin.tie(0); ll n, m; cin >> n >> m; M a; // b = 0 -> 01 // b = 1 -> 10 auto count1 = [&](int k0, int b0) -> mint { mint dp[2]; dp[0] = 1; rrep(k, 60) { mint ndp[2]; int bit = m >> k & 1; rep(state, 2) rep(bj, 2) { if (k == k0 && bj != b0) continue; if (state || bj < bit) ndp[1] += dp[state]; else if (bj == bit) ndp[state] += dp[state]; } swap(dp, ndp); } return dp[1]; }; auto count2 = [&](int k1, int b1, int k2, int b2) -> mint { if (k1 == k2) { if (b1 == b2) return mint(); return count1(k1, b2); } mint dp[2]; dp[0] = 1; rrep(k, 60) { mint ndp[2]; int bit = m >> k & 1; rep(state, 2) rep(bj, 2) { if (k == k1 && bj != !b1) continue; if (k == k2 && bj != b2) continue; if (state || bj < bit) ndp[1] += dp[state]; else if (bj == bit) ndp[state] += dp[state]; } swap(dp, ndp); } return dp[1]; }; rep(k1, 60) rep(b1, 2) { rep(k2, 60) rep(b2, 2) { a[2 * k1 + b1][2 * k2 + b2] = count2(k1, b1, k2, b2) * (1LL << k2); } } a.inplace_pow(n - 2); mint ans; rep(k1, 60) rep(b1, 2) { rep(k2, 60) rep(b2, 2) { mint v = a[2 * k1 + b1][2 * k2 + b2]; v *= 1LL << k1; v *= count1(k1, b1) * count1(k2, !b2); ans += v; } } cout << ans.val() << '\n'; }