#define ATCODER #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ld = long double; using pll = pair; using pdd = pair; //template using pq = priority_queue, greater>; #define FOR(i, a, b) for(ll i=(a); i<(b);i++) #define REP(i, n) for(ll i=0; i<(n);i++) #define ROF(i, a, b) for(ll i=(b-1); i>=(a);i--) #define PER(i, n) for(ll i=n-1; i>=0;i--) #define REPREP(i,j,a,b) for(ll i=0;i > #define VV2(type,n,m,val) vector< vector > val;val.resize(n);for(ll i;i #define VEC(type,n,val) vector val;val.resize(n) #define VL vector #define VVL vector< vector > #define VP vector< pair > #define SZ size() #define all(i) begin(i),end(i) #define SORT(i) sort(all(i)) #define BITI(i) (1<>i) & 1) != 0) #define ALLBIT(n) (ll(1)<v?v:n #define MP(a,b) make_pair(a,b) #define DET2(x1,y1,x2,y2) x1*y2-x2*y1 #define DET3(x1,y1,z1,x2,y2,z2,x3,y3,z3) x1*y2*z3+x2*y3*z1+x3*y1*z2-z1*y2*x3-z2*y3*x1-z3*y1*x2 #define INC(a) for(auto& v:a)v++; #define DEC(a) for(auto& v:a)v--; #define SQU(x) (x)*(x) #define L0 ll(0) #ifdef ATCODER #include using namespace atcoder; using mint = modint1000000007; using mint2 = modint998244353; #endif template vector read(size_t n) { vector ts(n); for (size_t i = 0; i < n; i++) cin >> ts[i]; return ts; } template void read_tuple_impl(TV&) {} template void read_tuple_impl(TV& ts) { get(ts).emplace_back(*(istream_iterator(cin))); read_tuple_impl(ts); } template decltype(auto) read_tuple(size_t n) { tuple...> ts; for (size_t i = 0; i < n; i++) read_tuple_impl(ts); return ts; } using val = ll; using func = ll; val op(val a, val b) { return min(a, b); } val e() { return 1e18; } val mp(func f, val a) { if (f == -1) return a; return f; } func comp(func f, func g) { if (f == -1) return g; return f; } func id() { return -1; } ll di[4] = { 1,0,-1,0 }; ll dj[4] = { 0,1,0,-1 }; //ll di[4] = { -1,-1,1,1 }; //ll dj[4] = { -1,1,-1,1 }; ll di8[8] = { 0,-1,-1,-1,0,1,1,1 }; ll dj8[8] = { -1,-1,0,1,1,1,0,-1 }; template T Combi(ll a, ll b, vector& fact, vector& rfact) { if (a < 0 || b < 0 || a < b) return 0; return fact[a] / (fact[b] * fact[a - b]); } void solve() { ll t; cin >> t; ll MAX_N = 200000; ll MAX_M = 200000; ll rn = sqrt(MAX_N); vector f(MAX_N * 2 + 101, 1), rf(MAX_N * 2 + 101, 1); mint2 half = mint2(1) / 2; REP(i, MAX_N * 2 + 100) { f[i + 1] = f[i] * (i + 1); rf[i + 1] = mint2(1) / f[i + 1]; } vector> nmi(t); REP(i, t) { ll n, m; cin >> n >> m; nmi[i] = make_tuple(n, m, i); } SORT(nmi); vector ans(t); ll mx = 0; ll nnm = 0; while (mx < MAX_N) { vector> mni; while (nnm < t) { auto [n, m, i] = nmi[nnm]; if (n >= mx + rn + 1) break; if (m * 2 > n) mni.emplace_back(m, n, i); nnm++; } SORT(mni); mint2 sum = 0; ll fsm = (mx + 1) / 2; ll mnid = 0; FOR(mm, fsm, MAX_M + 1) { if (mnid == mni.size()) break; while (mnid < mni.size()) { auto [m, n, i] = mni[mnid]; if (m != mm) break; mint2 now = sum; REP(i, n - mx - 1) { now = (Combi(m * 2, mx + i + 2, f, rf) - now) * half; } ans[i] = now; mnid++; } sum += Combi(mm * 2, mx, f, rf); } mx += rn; } REP(i, t) { cout << ans[i].val() << "\n"; } return; } int main() { ll t = 1; //cin >> t; while (t--) { solve(); } return 0; }