#include using namespace std; //#define int long long //TEMPLATE START---------------8<---------------8<---------------8<---------------8<---------------// typedef long long ll; typedef long double ld; typedef pair pii; typedef pair pll; typedef vector vi; typedef vector vl; typedef vector vst; typedef vector vb; typedef vector vld; typedef vector vpii; typedef vector vpll; typedef vector > vvi; const int INF = (0x7FFFFFFFL); const ll INFF = (0x7FFFFFFFFFFFFFFFL); const string ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const int MOD = 1e9 + 7; const int MODD = 998244353; const string alphabet = "abcdefghijklmnopqrstuvwxyz"; const double PI = acos(-1.0); const double EPS = 1e-9; const string Alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"; int dx[9] = { 1, 0, -1, 0, 1, -1, -1, 1, 0 }; int dy[9] = { 0, 1, 0, -1, -1, -1, 1, 1, 0 }; #define ln '\n' #define scnaf scanf #define sacnf scanf #define sancf scanf #define SS(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__); template void MACRO_VAR_Scan(T& t){cin >> t;}template void MACRO_VAR_Scan(First& first, Rest&...rest){cin >> first;MACRO_VAR_Scan(rest...);} #define SV(type,c,n) vector c(n);for(auto& i:c)cin >> i; #define SVV(type,c,n,m) vector> c(n,vector(m));for(auto& r:c)for(auto& i:r)cin >> i; templateostream &operator<<(ostream &o,const pair&j){o<<"{"<ostream &operator<<(ostream &o,const map&j){o<<"{";for(auto t=j.begin();t!=j.end();++t)o<<(t!=j.begin()?", ":"")<<*t;o<<"}";return o;} templateostream &operator<<(ostream &o,const set&j){o<<"{";for(auto t=j.begin();t!=j.end();++t)o<<(t!=j.begin()?", ":"")<<*t;o<<"}";return o;} templateostream &operator<<(ostream &o,const vector&j){o<<"{";for(int i=0;i<(int)j.size();++i)o<<(i>0?", ":"")< int print(Head&& head){cout << head;print();return 0;} template int print(Head&& head,Tail&&... tail){cout<(tail)...);return 0;} inline int debug(void){cerr << endl; return 0;} template int debug(Head&& head){cerr << head;debug();return 0;} template int debug(Head&& head,Tail&&... tail){cerr<(tail)...);return 0;} template void PA(T &a){int ASIZE=sizeof(a)/sizeof(a[0]);for(int ii=0;ii void PV(T &v){int VSIZE=v.size();for(int ii=0;ii void sankou(bool x,A a,B b){cout<<((x)?(a):(b))<=ll(b);--i) #define RREP(...) _overload3(__VA_ARGS__,RREPI,_RREP,)(__VA_ARGS__) #define EACH(e,v) for(auto& e : v) #define PERM(v) sort((v).begin(),(v).end());for(bool c##p=1;c##p;c##p=next_permutation((v).begin(),(v).end())) #define ADD(a,b) a=(a+ll(b))%MOD #define MUL(a,b) a=(a*ll(b))%MOD inline ll MOP(ll x,ll n,ll m=MOD){ll r=1;while(n>0){if(n&1)(r*=x)%=m;(x*=x)%=m;n>>=1;}return r;} inline ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}inline ll lcm(ll a,ll b){return a*b/gcd(a,b);}inline ll POW(ll a,ll b){ll c=1ll;do{if(b&1)c*=1ll*a;a*=1ll*a;}while(b>>=1);return c;} template inline bool between(T x,A a,B b) {return ((a<=x)&&(x inline T sqr(T x){return x*x;} template inline bool chmax(A &a,const B &b){if(a inline bool chmin(A &a,const B &b){if(a>b){a=b;return 1;}return 0;} #define tmax(x,y,z) max((x),max((y),(z))) #define tmin(x,y,z) min((x),min((y),(z))) #define PB push_back #define MP make_pair #define MT make_tuple #define all(v) (v).begin(),(v).end() #define rall(v) (v).rbegin(),(v).rend() #define SORT(v) sort((v).begin(),(v).end()) #define RSORT(v) sort((v).rbegin(),(v).rend()) #define EXIST(s,e) (find((s).begin(),(s).end(),(e))!=(s).end()) #define EXISTST(s,c) (((s).find(c))!=string::npos) #define POSL(x,val) (lower_bound(x.begin(),x.end(),val)-x.begin()) #define POSU(x,val) (upper_bound(x.begin(),x.end(),val)-x.begin()) #define GEQ(x,val) (int)(x).size() - POSL((x),(val)) #define GREATER(x,val) (int)(x).size() - POSU((x),(val)) #define LEQ(x,val) POSU((x),(val)) #define LESS(x,val) POSL((x),(val)) #define SZV(a) int((a).size()) #define SZA(a) sizeof(a)/sizeof(a[0]) #define ZERO(a) memset(a,0,sizeof(a)) #define MINUS(a) memset(a,0xff,sizeof(a)) #define MEMINF(a) memset(a,0x3f,sizeof(a)) #define FILL(a,b) memset(a,b,sizeof(a)) #define UNIQUE(v) sort((v).begin(),(v).end());(v).erase(unique((v).begin(),(v).end()),(v).end()) struct abracadabra{ abracadabra(){ cin.tie(0); ios::sync_with_stdio(0); cout << fixed << setprecision(20); cerr << fixed << setprecision(5); }; } ABRACADABRA; //TEMPLATE END---------------8<---------------8<---------------8<---------------8<---------------// /* ・ModInt [備考] Mod演算のための構造体 [使用例] modint M; // 剰余系MOD(1e9+7)における演算ができる ModInt N; // 剰余系modにおける演算ができる */ template< int MODULO > struct ModInt { using uint32 = uint_fast32_t; using uint64 = uint_fast64_t; uint64 x; ModInt() : x(0) {} ModInt(uint64 y) : x(set(y % MODULO + MODULO)) {} static uint64 set(const uint64 &y) { return (y < MODULO) ? y : y - MODULO; } static ModInt make(const uint64 &y) { ModInt ret = y; return ret; } ModInt operator+(const ModInt &m) const { return make(set(x + m.x)); } ModInt operator-(const ModInt &m) const { return make(set(x + MODULO - m.x)); } ModInt operator*(const ModInt &m) const { return make(x * m.x % MODULO); } ModInt operator/(const ModInt &m) const { return make(x) * ~make(m.x); } ModInt &operator+=(const ModInt &m) { return *this = *this + m; } ModInt &operator-=(const ModInt &m) { return *this = *this - m; } ModInt &operator*=(const ModInt &m) { return *this = *this * m; } ModInt &operator/=(const ModInt &m) { return *this = *this / m; } ModInt &operator^=(const uint64 &y) { return *this = *this ^ y; } ModInt operator~ () const { return *this ^ (MODULO - 2); } ModInt operator- () const { return make(set(MODULO - x)); } ModInt operator! () const { init(uint32(*this)); return fact[uint32(*this)]; } ModInt operator& () const { init(uint32(*this)); return finv[uint32(*this)]; } ModInt operator++() { return *this = make(set(x + 1)); } ModInt operator--() { return *this = make(set(x + MODULO - 1)); } bool operator==(const ModInt &m) const { return x == m.x; } bool operator!=(const ModInt &m) const { return x != m.x; } bool operator< (const ModInt &m) const { return x < m.x; } bool operator<=(const ModInt &m) const { return x <= m.x; } bool operator> (const ModInt &m) const { return x > m.x; } bool operator>=(const ModInt &m) const { return x >= m.x; } explicit operator bool() const { return x; } explicit operator uint64() const { return x; } ModInt operator^(uint64 y) const { uint64 t = x, u = 1; while (y) { if (y & 1) (u *= t) %= MODULO; (t *= t) %= MODULO; y >>= 1; } return make(u); } friend ostream &operator<<(ostream &os, const ModInt< MODULO > &m) { return os << m.x; } friend istream &operator>>(istream &is, ModInt< MODULO > &m) { uint64 y; is >> y; m = make(y); return is; } static vector< ModInt > fact, finv, invs; static void init(uint32 n) { uint32 m = fact.size(); if (n < m) return; fact.resize(n + 1, 1); finv.resize(n + 1, 1); invs.resize(n + 1, 1); if (m == 0) m = 1; for (uint32 i = m; i <= n; ++i) fact[i] = fact[i - 1] * ModInt(i); finv[n] = ModInt(1) / fact[n]; for (uint32 i = n; i >= m; --i) finv[i - 1] = finv[i] * make(i); for (uint32 i = m; i <= n; ++i) invs[i] = finv[i] * fact[i - 1]; } static ModInt C(uint64 n, uint64 r) { if (r == 0) return make(1); if (r < 0) return make(0); if (n < 0) return make(r & 1 ? MODULO - 1 : 1) * C(-n + r - 1, r); if (n == 0 || n < r) return make(0); init(n); return fact[n] * finv[n - r] * finv[r]; } static ModInt P(uint64 n, uint64 r) { if (n < r || r < 0) return make(0); init(n); return fact[n] * finv[n - r]; } static ModInt H(uint64 n, uint64 r) { if (n < 0 || r < 0) return make(0); if (!n && !r) return make(1); init(n + r - 1); return C(n + r - 1, r); } static ModInt montmort(uint32 n) { ModInt res; init(n); for (uint32 k = 2; k <= n; ++k) { if (k & 1) res -= finv[k]; else res += finv[k]; } return res *= fact[n]; } static ModInt LagrangePolynomial(vector &y, ModInt t) { uint32 n = y.size() - 1; if (t.x <= n) return y[t.x]; init(n + 1); ModInt res, num(1); for (uint32 i = 0; i <= n; ++i) num *= t - make(i); for (uint32 i = 0; i <= n; ++i) { ModInt tmp = y[i] * num / (t - make(i)) * finv[i] * finv[n - i]; if ((n - i) & 1) res -= tmp; else res += tmp; } return res; } }; template< int MODULO > vector> ModInt< MODULO >::fact = vector>(); template< int MODULO > vector> ModInt< MODULO >::finv = vector>(); template< int MODULO > vector> ModInt< MODULO >::invs = vector>(); using modint = ModInt< MOD >; using mint = ModInt< 17 >; /* ・行列演算 [使用例] Matrix mat(n,m); // n行m列の行列を定義 mat[i][j]; // i行j列目の要素を取得 mat.determinant(); // matの行列式を計算 mat ^= k; // matのk乗を計算 */ template< class T > struct Matrix { vector< vector< T > > A; Matrix() {} Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {} Matrix(size_t n) : A(n, vector< T >(n, 0)) {}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector< T > &operator[](int k) const { return (A.at(k)); } inline vector< T > &operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix mat(n); for (int i = 0; i < n; ++i) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector< vector< T > > C(n, vector< T >(m, 0)); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) for(int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(height()); while (k > 0) { if (k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } friend ostream &operator<<(ostream &os, Matrix &p) { size_t n = p.height(), m = p.width(); for (int i = 0; i < n; i++) { os << "["; for (int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() { Matrix B(*this); assert(width() == height()); T ret = 1; for (int i = 0; i < width(); i++) { int idx = -1; for (int j = i; j < width(); j++) if (B[j][i] != 0) idx = j; if (idx == -1) return (0); if (i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for (int j = 0; j < width(); j++) B[i][j] /= vv; for (int j = i + 1; j < width(); j++) { T a = B[j][i]; for (int k = 0; k < width(); k++) B[j][k] -= B[i][k] * a; } } return (ret); } }; signed main() { Matrix< mint > mat(4, 4); mat[0][1] = 1; mat[1][2] = 1; mat[2][3] = 1; REP(i, 4) mat[3][i] = 1; SS(ll, Q); SV(ll, N, Q); EACH(n, N) { if (n <= 3) cout << 0 << endl; else if (n == 4) cout << 1 << endl; else { cout << (mat ^ n - 4)[3][3] << endl; } } }