/** * author: otera **/ #include #ifndef OTERA_MODINT #define OTERA_MODINT 1 #include namespace otera { using modint107 = atcoder::modint1000000007; using modint998 = atcoder::modint998244353; using modint = atcoder::modint; }; //namespace otera std::ostream& operator<<(std::ostream& out, const atcoder::modint1000000007 &e) { out << e.val(); return out; } std::ostream& operator<<(std::ostream& out, const atcoder::modint998244353 &e) { out << e.val(); return out; } std::ostream& operator<<(std::ostream& out, const atcoder::modint &e) { out << e.val(); return out; } #endif // OTERA_MODINT namespace otera{ template class factorial { public: factorial() {} factorial(int n) { ensure(n); } T com(const int n, const int k) { if(n == k) return 1; if(n < k or n < 0 or k < 0) return 0; ensure(n); return fact_[n] * finv_[k] * finv_[n - k]; } T fact(const int n) { if(n < 0) return 0; ensure(n); return fact_[n]; } T inv(const int n) { if(n < 0) return 0; ensure(n); return inv_[n]; } T finv(const int n) { if(n < 0) return 0; ensure(n); return finv_[n]; } private: static std::vector fact_, inv_, finv_; int MOD = T::mod(); void ensure(const int n) { int sz = fact_.size(); if(n + 1 <= sz) return; int next_sz = std::max(n + 1, sz * 2); fact_.resize(next_sz), inv_.resize(next_sz), finv_.resize(next_sz); for(int i = sz; i < next_sz; ++ i) { fact_[i] = fact_[i - 1] * i; inv_[i] = -inv_[MOD % i] * (MOD / i); finv_[i] = finv_[i - 1] * inv_[i]; } } }; template std::vector factorial::fact_ {1, 1}; template std::vector factorial::inv_ {1, 1}; template std::vector factorial::finv_ {1, 1}; } // namespace otera using namespace std; #define int long long using ll = long long; using ld = long double; using ull = unsigned long long; using int128_t = __int128_t; #define repa(i, n) for(int i = 0; i < n; ++ i) #define repb(i, a, b) for(int i = a; i < b; ++ i) #define repc(i, a, b, c) for(int i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define rep(...) overload4(__VA_ARGS__, repc, repb, repa)(__VA_ARGS__) #define rep1a(i, n) for(int i = 0; i <= n; ++ i) #define rep1b(i, a, b) for(int i = a; i <= b; ++ i) #define rep1c(i, a, b, c) for(int i = a; i <= b; i += c) #define rep1(...) overload4(__VA_ARGS__, rep1c, rep1b, rep1a)(__VA_ARGS__) #define rev_repa(i, n) for(int i=n-1;i>=0;i--) #define rev_repb(i, a, b) assert(a > b);for(int i=a;i>b;i--) #define rev_rep(...) overload3(__VA_ARGS__, rev_repb, rev_repa)(__VA_ARGS__) #define rev_rep1a(i, n) for(int i=n;i>=1;i--) #define rev_rep1b(i, a, b) assert(a >= b);for(int i=a;i>=b;i--) #define rev_rep1(...) overload3(__VA_ARGS__, rev_rep1b, rev_rep1a)(__VA_ARGS__) typedef pair P; typedef pair LP; #define pb push_back #define pf push_front #define ppb pop_back #define ppf pop_front #define eb emplace_back #define fr first #define sc second #define all(c) c.begin(),c.end() #define rall(c) c.rbegin(), c.rend() #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define Sort(a) sort(all(a)) #define Rev(a) reverse(all(a)) #define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a)) #define si(c) (int)(c).size() inline ll popcnt(ull a){ return __builtin_popcountll(a); } #define kth_bit(x, k) ((x>>k)&1) #define unless(A) if(!(A)) ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } ll intpow(ll a, ll b, ll m) {ll ans = 1; while(b){ if(b & 1) (ans *= a) %= m; (a *= a) %= m; b /= 2; } return ans; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } #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 using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; template using umap = unordered_map; template void scan(T& a){ cin >> a; } template void scan(vector& a){ for(auto&& i : a) scan(i); } void in(){} template void in(Head& head, Tail&... tail){ scan(head); in(tail...); } void print(){ cout << ' '; } template void print(const T& a){ cout << a; } template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout << ' '; print(*i); } } int out(){ cout << '\n'; return 0; } template int out(const T& t){ print(t); cout << '\n'; return 0; } template int out(const Head& head, const Tail&... tail){ print(head); cout << ' '; out(tail...); return 0; } #define CHOOSE(a) CHOOSE2 a #define CHOOSE2(a0,a1,a2,a3,a4,x,...) x #define debug_1(x1) cout<<#x1<<": "< bc; void solve() { INT(n, m); mint ans = mint(m).pow(2 * n + 1); ans -= mint(m) * mint(m - 1).pow(2 * n); for(int i = 2; i <= m; ++ i) { if(i - 1 > n) break; ans -= bc.com(m, i) * bc.com(n, i - 1) * bc.fact(i - 1) * mint(i).pow(i - 2) * mint(2).pow(i - 1) * mint(m - i).pow(2 * n - 2 * (i - 1)); } out(ans); } signed main() { int testcase = 1; // in(testcase); while(testcase--) solve(); return 0; }