#include using namespace std; using ll = long long; using ld = long double; using ull = unsigned long long; using uint = unsigned; using pii = pair; using pll = pair; using pdd = pair; using tuplis = array; template using pq = priority_queue, greater>; const ll LINF=0x1fffffffffffffff; const ll MINF=0x7fffffffffff; const int INF=0x3fffffff; const int MOD=1000000007; const int MODD=998244353; const ld DINF=numeric_limits::infinity(); const ld EPS=1e-9; const ld PI=3.1415926535897932; const ll dx[] = {0, 1, 0, -1, 1, -1, 1, -1}; const ll dy[] = {1, 0, -1, 0, 1, 1, -1, -1}; #define overload5(a,b,c,d,e,name,...) name #define overload4(a,b,c,d,name,...) name #define overload3(a,b,c,name,...) name #define rep1(n) for(ll i=0;i(a);) #define rrep4(i,a,b,c) for(ll i=(a)+((b)-(a)-1)/(c)*(c);i>=(a);i-=c) #define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__) #define each1(i,a) for(auto&&i:a) #define each2(x,y,a) for(auto&&[x,y]:a) #define each3(x,y,z,a) for(auto&&[x,y,z]:a) #define each4(w,x,y,z,a) for(auto&&[w,x,y,z]:a) #define each(...) overload5(__VA_ARGS__,each4,each3,each2,each1)(__VA_ARGS__) #define all1(i) begin(i),end(i) #define all2(i,a) begin(i),begin(i)+a #define all3(i,a,b) begin(i)+a,begin(i)+b #define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__) #define rall1(i) rbegin(i),rend(i) #define rall2(i,a) rbegin(i),rbegin(i)+a #define rall3(i,a,b) rbegin(i)+a,rbegin(i)+b #define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) #define dsum(...) accumulate(all(__VA_ARGS__),0.0L) #define Msum(...) accumulate(all(__VA_ARGS__),mint{}) #define elif else if #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__) #define vec(type,name,...) vectorname(__VA_ARGS__) #define VEC(type,name,size) vectorname(size);in(name) #define vv(type,name,h,...) vector name(h,vector(__VA_ARGS__)) #define VV(type,name,h,w) vector name(h,vector(w));in(name) #define vvv(type,name,h,w,...) vector name(h,vector(w,vector(__VA_ARGS__))) template auto min(const T& a){ return *min_element(all(a)); } template auto max(const T& a){ return *max_element(all(a)); } template ll count(const T& a, const U& b){ return count(all(a), b); } template ll count_if(const T& a, F b){ return count_if(all(a), b); } template void filter(T& a, F b){ a.erase(remove_if(all(a), not_fn(b)), a.end()); } template> void sor(T& a, F b = F{}){ sort(all(a), b); } template void rev(T& a){ reverse(all(a)); } template void uniq(T& a){ sor(a); a.erase(unique(all(a)), end(a)); } ll popcnt(ull a){ return __builtin_popcountll(a); } ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } template T div_floor(T a, T b) { return a / b - ((a ^ b) < 0 && a % b); } template T div_ceil(T a, T b) { return a / b + ((a ^ b) > 0 && a % b); } template bool chmin(T& a, const T& b){ if(a <= b) return 0; a = b; return 1; } template bool chmax(T& a, const T& b){ if(a >= b) return 0; a = b; return 1; } template bool chmin(T& a, const U& b){ return chmin(a, (T)b); } template bool chmax(T& a, const U& b){ return chmax(a, (T)b); } vector iota(ll n, ll begin = 0){ vector a(n); iota(a.begin(), a.end(), begin); return a; } vector factor(ull x){ vector ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; } vector divisor(ull x){ vector ans; for(ull i = 1; i * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; } template unordered_map press(vector a){ uniq(a); unordered_map ans; rep(a.size()) ans[a[i]] = i; return ans; } template auto run_press(const T& a){ vector, ll>> ans; each(x, a){ if(ans.empty() || ans.back().first != x) ans.emplace_back(x, 1); else ans.back().second++; } return ans; } template void in(Ts&... t); [[maybe_unused]] void print(){} template void print(const T& t, const Ts&... ts); template void out(const Ts&... ts){ print(ts...); cout << '\n'; } namespace IO{ #define VOID(a) decltype(void(a)) struct S{ S(){ cin.tie(nullptr)->sync_with_stdio(0); fixed(cout).precision(12); } }S; template struct P : P{}; template<> struct P<0>{}; template void i(T& t){ i(t, P<3>{}); } void i(vector::reference t, P<3>){ int a; i(a); t = a; } template auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template void ituple(T& t, index_sequence){ in(get(t)...); } template auto i(T& t, P<0>) -> VOID(tuple_size{}){ ituple(t, make_index_sequence::value>{}); } template void o(const T& t){ o(t, P<4>{}); } template void o(const char (&t)[N], P<4>){ cout << t; } template void o(const T (&t)[N], P<3>){ o(t[0]); for(size_t i = 1; i < N; i++){ o(' '); o(t[i]); } } template auto o(const T& t, P<2>) -> VOID(cout << t){ cout << t; } template auto o(const T& t, P<1>) -> VOID(begin(t)){ bool first = 1; for(auto&& x : t) { if(first) first = 0; else o(' '); o(x); } } template void otuple(const T& t, index_sequence){ print(get(t)...); } template auto o(T& t, P<0>) -> VOID(tuple_size{}){ otuple(t, make_index_sequence::value>{}); } #undef VOID } #define unpack(a) (void)initializer_list{(a, 0)...} template void in(Ts&... t){ unpack(IO::i(t)); } template void print(const T& t, const Ts&... ts){ IO::o(t); unpack(IO::o((cout << ' ', ts))); } #undef unpack #ifdef DEBUG ll __lg(ull x){ return 63 - __builtin_clzll(x); } #define debug(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); } #else #define debug(...) void(0) #endif #define YESNO(yes,no) void yes(bool i = 1){ out(i?#yes:#no); } void no(){ out(#no); } YESNO(first, second) YESNO(First, Second) YESNO(Yes, No) YESNO(YES, NO) YESNO(possible, impossible) YESNO(Possible, Impossible) YESNO(POSSIBLE, IMPOSSIBLE) void Case(ll i){ print("Case #"); print(i); print(": "); } template class static_modint { using mint = static_modint; uint32_t _v = 0; static constexpr bool prime = []() -> bool { if (m == 1) return 0; if (m == 2 || m == 7 || m == 61) return 1; if (m % 2 == 0) return 0; uint32_t d = m - 1; while (d % 2 == 0) d /= 2; for (uint32_t a : {2, 7, 61}) { uint32_t t = d; mint y = mint(a).pow(t); while (t != m - 1 && y != 1 && y != m - 1) { y *= y; t <<= 1; } if (y != m - 1 && t % 2 == 0) return 0; } return 1; }(); static constexpr pair inv_gcd(int32_t a, int32_t b) { if (a == 0) return {b, 0}; int32_t s = b, t = a, m0 = 0, m1 = 1; while (t) { const int32_t u = s / t; s -= t * u; m0 -= m1 * u; swap(s, t); swap(m0, m1); } if (m0 < 0) m0 += b / s; return {s, m0}; } public: static constexpr mint raw(uint32_t v) { mint a; a._v = v; return a; } constexpr static_modint() {} template constexpr static_modint(T v) { static_assert(is_integral_v, "T is not integral type."); if constexpr (is_signed_v) { int64_t x = int64_t(v % int64_t(m)); if (x < 0) x += m; _v = uint32_t(x); } else _v = uint32_t(v % m); } static constexpr uint32_t mod() { return m; } constexpr uint32_t val() const { return _v; } constexpr mint& operator++() { return *this += 1; } constexpr mint& operator--() { return *this -= 1; } constexpr mint operator++(int) { mint res = *this; ++*this; return res; } constexpr mint operator--(int) { mint res = *this; --*this; return res; } constexpr mint& operator+=(mint rhs) { if (_v >= m - rhs._v) _v -= m; _v += rhs._v; return *this; } constexpr mint& operator-=(mint rhs) { if (_v < rhs._v) _v += m; _v -= rhs._v; return *this; } constexpr mint& operator*=(mint rhs) { return *this = *this * rhs; } constexpr mint& operator/=(mint rhs) { return *this *= rhs.inv(); } constexpr mint operator+() const { return *this; } constexpr mint operator-() const { return mint{} - *this; } constexpr mint pow(long long n) const { assert(0 <= n); if(n == 0) return 1; mint x = *this, r = 1; while (1) { if (n & 1) r *= x; n >>= 1; if (n == 0) return r; x *= x; } } constexpr mint inv() const { if constexpr (prime) { assert(_v); return pow(m - 2); } else { auto eg = inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend constexpr mint operator+(mint lhs, mint rhs) { return lhs += rhs; } friend constexpr mint operator-(mint lhs, mint rhs) { return lhs -= rhs; } friend constexpr mint operator*(mint lhs, mint rhs) { return uint64_t(lhs._v) * rhs._v; } friend constexpr mint operator/(mint lhs, mint rhs) { return lhs /= rhs; } friend constexpr bool operator==(mint lhs, mint rhs) { return lhs._v == rhs._v; } friend constexpr bool operator!=(mint lhs, mint rhs) { return lhs._v != rhs._v; } }; using mint = static_modint; istream& operator>>(istream& in, mint& x) { long long a; in >> a; x = a; return in; } ostream& operator<<(ostream& out, mint x) { return out << x.val(); } constexpr mint operator""_M(unsigned long long x) { return x; } constexpr uint32_t fact_mx = min(1e6, mint::mod() - 1); mint fac[fact_mx + 1], inv[fact_mx + 1]; struct factorial { factorial() { fac[0] = 1; for(uint32_t i = 1; i <= fact_mx; i++) fac[i] = fac[i - 1] * mint::raw(i); inv[fact_mx] = fac[fact_mx].inv(); for(uint32_t i = fact_mx; i; i--) inv[i - 1] = inv[i] * mint::raw(i); } } factorial; mint inverse(long long n) { return inv[n] * fac[n - 1]; } mint perm(long long n, long long r) { if(n < r || r < 0) return 0; if(n > fact_mx) [[unlikely]] { mint ans = 1, x = n; while(r--) ans *= x--; return ans; } return fac[n] * inv[n - r]; } mint comb(long long n, long long r) { if(n < r || r < 0) return 0; r = min(r, n - r); const mint ans = perm(n, r); return ans * inv[r]; } template mint comb(long long n, T... rs) { if(n < 0) return 0; mint ans = fac[n]; long long rn = n; for(long long r : {rs...}) { if(r < 0) return 0; ans *= inv[r]; rn -= r; } if(rn < 0) return 0; return ans * inv[rn]; } mint Mcomb(long long n, long long r){ return comb(n + r - 1, r); } // r balls into n boxes int main(){ LL(n,k); if(n==1){ out(vector{1,1,3,3,3,1,1}[k]); return 0; } mint ans=0; ans+=comb(2*n+4,k); if(n%2==0){ k/=2; ans+=3*comb(n+2,k); } else{ k/=2; ans+=2*comb(n+1,k); } out(ans/4); }