#include #include //#define _GLIBCXX_DEBUG #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #define rep(i, n) for (int i = 0; i < (int)(n); i++) using namespace std; using namespace atcoder; using ll = long long; using pll = pair; using pii = pair; long long pow(long long x, long long n, ll mod) { long long ret = 1; while (n > 0) { if (n & 1) ret *= x; // n の最下位bitが 1 ならば x^(2^i) をかける ret %= mod; x *= x; x %= mod; n >>= 1; // n を1bit 左にずらす } return ret; } const int MAX = 310000; const int MOD = 998244353; long long fac[MAX], finv[MAX], inv[MAX]; // テーブルを作る前処理 void COMinit() { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < MAX; i++){ fac[i] = fac[i - 1] * i % MOD; inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD; finv[i] = finv[i - 1] * inv[i] % MOD; } } // 二項係数計算 long long COM(int n, int k){ if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD; } int main() { cin.tie(0); ios::sync_with_stdio(false); COMinit(); vector> R(0, vector(0)); int N_max = 200000; int bsize = 400; for (int n = 0; n < N_max + 1; n += bsize) { vector C(1, 0); rep(j, n+1) { ll c_last = C[C.size() - 1]; C.push_back((c_last + COM(n, j)) % MOD); } R.push_back(C); } int T; cin >> T; rep(t, T) { int N, M; cin >> N >> M; ll X = (pow(2, N, MOD) - 1) % MOD; N--; ll ans = 0; if (N < bsize) { rep(j, M) { ans += COM(N, j); ans = (ans + MOD) % MOD; } cout << (X * ans) % MOD << "\n"; } else { int NN = bsize * (N / bsize); int ii = N / bsize; int K = N - NN; int l = M - K; int r = M; if (l >= 1 && r <= NN) { rep(j, K+1) { ans += (R[ii][l + j] * COM(K, j)) % MOD; ans = (ans + MOD) % MOD; } } else { if (l < 1) { rep(j, M) { ans += COM(N, j); ans = (ans + MOD) % MOD; } } else { ans = pow(2, N, MOD); rep(j, N-M+1) { ans -= COM(N, N-j); ans = (ans + MOD) % MOD; } } } cout << (X * ans) % MOD << "\n"; } /* // guchoku ll ans2 = 0; rep(j, M) { ans2 += COM(N, j); ans2 %= MOD; } cout << (X * ans2) % MOD << "\n"; */ } }