#include "bits/stdc++.h" using namespace std; #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) static const int INF = 0x3f3f3f3f; static const long long INFL = 0x3f3f3f3f3f3f3f3fLL; typedef vector vi; typedef pair pii; typedef vector > vpii; typedef long long ll; template static void amin(T &x, U y) { if (y < x) x = y; } template static void amax(T &x, U y) { if (x < y) x = y; } template struct ModInt { static const int Mod = MOD; unsigned x; ModInt() : x(0) { } ModInt(signed sig) { int sigt = sig % MOD; if (sigt < 0) sigt += MOD; x = sigt; } ModInt(signed long long sig) { int sigt = sig % MOD; if (sigt < 0) sigt += MOD; x = sigt; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; } ModInt &operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; } ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { signed a = x, b = MOD, u = 1, v = 0; while (b) { signed t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } if (u < 0) u += Mod; ModInt res; res.x = (unsigned)u; return res; } bool operator==(ModInt that) const { return x == that.x; } bool operator!=(ModInt that) const { return x != that.x; } ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; } }; typedef ModInt<17> mint; mint linearlyRecurrentSequenceValue(long long K, const vector &initValues, const vector &annPoly) { assert(K >= 0); if (K < (int)initValues.size()) return initValues[(int)K]; int d = (int)annPoly.size() - 1; assert(d >= 0); assert(annPoly[d].get() == 1); assert(d <= (int)initValues.size()); if (d == 0) return mint(); vector coeffs(d), square; coeffs[0] = 1; int l = 0; while ((K >> l) > 1) ++ l; for (; l >= 0; -- l) { square.assign(d * 2 - 1, mint()); for (int i = 0; i < d; ++ i) for (int j = 0; j < d; ++ j) square[i + j] += coeffs[i] * coeffs[j]; for (int i = d * 2 - 2; i >= d; -- i) { mint c = square[i]; if (c.x == 0) continue; for (int j = 0; j < d; ++ j) square[i - d + j] -= c * annPoly[j]; } for (int i = 0; i < d; ++ i) coeffs[i] = square[i]; if (K >> l & 1) { mint lc = coeffs[d - 1]; for (int i = d - 1; i >= 1; -- i) coeffs[i] = coeffs[i - 1] - lc * annPoly[i]; coeffs[0] = mint() - lc * annPoly[0]; } } mint res; for (int i = 0; i < d; ++ i) res += coeffs[i] * initValues[i]; return res; } mint linearlyRecurrentSequenceValue(long long K, const pair, vector > &seqPair) { return linearlyRecurrentSequenceValue(K, seqPair.first, seqPair.second); } int main() { int Q; while (~scanf("%d", &Q)) { rep(i, Q) { long long n; scanf("%lld", &n); mint ans = linearlyRecurrentSequenceValue(n, { { 0, 0, 0, 0, 1 },{ 0, -1, -1, -1, -1, 1 } }); printf("%d\n", ans.get()); } } return 0; }