#include using namespace std; using ll = long long; template using vt = vector; template using vvt = vector>; template using ttt = tuple; using tii = tuple; using vi = vector; #define rep(i,n) for(int i=0;i<(int)(n);i++) #define pb push_back #define mt make_tuple #define ALL(a) (a).begin(),(a).end() #define FST first #define SEC second #define DEB cerr<<"!"<0){if((n&1)==1)r=r*x%m;x=x*x%m;n>>=1;}return r%m;} inline ll lcm(ll d1, ll d2){return d1 / __gcd(d1, d2) * d2;} // IT 5000兆 欲しい /* Coding space */ unordered_map Inv; inline ll InvMod(ll n){ if(Inv.count(n)) return Inv[n]; return Inv[n] = pow(n, DIV - 2,DIV); } class FermatCombination{ public: vector factrial; // 階乗 vector inverse; // 逆元 FermatCombination(int size){ factrial.resize(size+1); inverse.resize(size+1); factrial[0] = 1; inverse[0] = 1; for(int i = 1; i < size+1; i++){ factrial[i] = factrial[i-1] * i % DIV; inverse[i] = pow(factrial[i],DIV-2,DIV); } } ll combination(int n, int k){ if(n < k) return 0; return factrial[n]* inverse[k] % DIV * inverse[n - k] % DIV; } ll permutation(int n, int k){ if(n < k) return 0; return factrial[n] * inverse[n-k] % DIV; } ll multi_choose(int n, int k){ if(n == 0 && k == 0) return 1; else return combination(n+k-1,k); } }; FermatCombination fc(10006); ll k,n; ll B[10005] = {}; bool used[10005] = {}; ll Bernoulli(int x){ //cerr <> n >> k; n %= DIV; ll s = 0; rep(j,k+1){ //cerr << s << " " << fc.combination(k+1,j) << " " << Bernoulli(j) << " " << pow(n+1,k-j+1,DIV) <