#include using namespace std; // 参照サイト. // 動的計画法でフィボナッチ数列の計算を速くする。 // https://yosuke-furukawa.hatenablog.com/entry/20120120/1327056359 typedef long long LL; // const LL MOD = 1e9 + 7; const LL MOD = 1e1 + 7; // 行列積のロジックを一部抽出した版. // @param p1 ~ q4: 行列の要素. // @return ret: 行列積の計算結果. LL matrixProduct(LL p1, LL p2, LL p3, LL p4, LL q1, LL q2, LL q3, LL q4){ LL ret = 0; ret += p1 * q1, ret %= MOD; ret += p2 * q2, ret %= MOD; ret += p3 * q3, ret %= MOD; ret += p4 * q4, ret %= MOD; return ret; } // Tetranacci sequence の 第N項 を計算. // A000078 Tetranacci numbers: // https://oeis.org/A000078 // ex. // MOD = 1e9 + 7 とすれば, // N = 20 なら tetranacciByMatrix(20) = 20569 % MOD = 20569 のように計算できる. // N = 37 なら tetranacciByMatrix(37) = 1439975216 % MOD = 439975209 のように計算できる. // @param N: 第N項. // @return ans: Tetranacci sequence の 第N項. LL tetranacciByMatrix(LL N){ // 0. N が 4以下ならば, 返却. if(N < 4) return 0; if(N == 4) return 1; // 1. N を 2で割っていく. // ex. N = 5以降で, はじめて, 行列積を適用する必要が出てくる. N -= 4; map m; while(N){ LL q = N >> 1; LL r = N & 1; m[q] = r; N >>= 1; } // for(auto &p : m) cout << p.first << " " << p.second << endl; // 2. 1. の 結果から, 逆算. // 第 0成分(1行1列): 1, 第 1成分(1行2列): 1, 第 2成分(1行3列): 1, 第 3成分(1行4列): 1 // 第 4成分(2行1列): 1, 第 5成分(2行2列): 0, 第 6成分(2行3列): 0, 第 7成分(2行4列): 0 // 第 8成分(3行1列): 0, 第 9成分(3行2列): 1, 第10成分(3行3列): 0, 第11成分(3行4列): 0 // 第12成分(4行1列): 0, 第13成分(4行2列): 0, 第14成分(4行3列): 1, 第15成分(4行4列): 0 LL ans[16] = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1}; for(auto &p : m){ if(p.first != 0){ LL t11 = ans[0], t12 = ans[1], t13 = ans[2], t14 = ans[3], t21 = ans[4], t22 = ans[5], t23 = ans[6], t24 = ans[7], t31 = ans[8], t32 = ans[9], t33 = ans[10], t34 = ans[11], t41 = ans[12], t42 = ans[13], t43 = ans[14], t44 = ans[15]; ans[0] = matrixProduct(t11, t12, t13, t14, t11, t21, t31, t41); ans[1] = matrixProduct(t11, t12, t13, t14, t12, t22, t32, t42); ans[2] = matrixProduct(t11, t12, t13, t14, t13, t23, t33, t43); ans[3] = matrixProduct(t11, t12, t13, t14, t14, t24, t34, t44); ans[4] = matrixProduct(t21, t22, t23, t24, t11, t21, t31, t41); ans[5] = matrixProduct(t21, t22, t23, t24, t12, t22, t32, t42); ans[6] = matrixProduct(t21, t22, t23, t24, t13, t23, t33, t43); ans[7] = matrixProduct(t21, t22, t23, t24, t14, t24, t34, t44); ans[8] = matrixProduct(t31, t32, t33, t34, t11, t21, t31, t41); ans[9] = matrixProduct(t31, t32, t33, t34, t12, t22, t32, t42); ans[10] = matrixProduct(t31, t32, t33, t34, t13, t23, t33, t43); ans[11] = matrixProduct(t31, t32, t33, t34, t14, t24, t34, t44); ans[12] = matrixProduct(t41, t42, t43, t44, t11, t21, t31, t41); ans[13] = matrixProduct(t41, t42, t43, t44, t12, t22, t32, t42); ans[14] = matrixProduct(t41, t42, t43, t44, t13, t23, t33, t43); ans[15] = matrixProduct(t41, t42, t43, t44, t14, t24, t34, t44); } if(p.second == 1){ LL t11 = ans[0], t12 = ans[1], t13 = ans[2], t14 = ans[3], t21 = ans[4], t22 = ans[5], t23 = ans[6], t24 = ans[7], t31 = ans[8], t32 = ans[9], t33 = ans[10], t34 = ans[11], t41 = ans[12], t42 = ans[13], t43 = ans[14], t44 = ans[15]; ans[0] = matrixProduct(t11, t12, t13, t14, 1, 1, 0, 0); ans[1] = matrixProduct(t11, t12, t13, t14, 1, 0, 1, 0); ans[2] = matrixProduct(t11, t12, t13, t14, 1, 0, 0, 1); ans[3] = matrixProduct(t11, t12, t13, t14, 1, 0, 0, 0); ans[4] = matrixProduct(t21, t22, t23, t24, 1, 1, 0, 0); ans[5] = matrixProduct(t21, t22, t23, t24, 1, 0, 1, 0); ans[6] = matrixProduct(t21, t22, t23, t24, 1, 0, 0, 1); ans[7] = matrixProduct(t21, t22, t23, t24, 1, 0, 0, 0); ans[8] = matrixProduct(t31, t32, t33, t34, 1, 1, 0, 0); ans[9] = matrixProduct(t31, t32, t33, t34, 1, 0, 1, 0); ans[10] = matrixProduct(t31, t32, t33, t34, 1, 0, 0, 1); ans[11] = matrixProduct(t31, t32, t33, t34, 1, 0, 0, 0); ans[12] = matrixProduct(t41, t42, t43, t44, 1, 1, 0, 0); ans[13] = matrixProduct(t41, t42, t43, t44, 1, 0, 1, 0); ans[14] = matrixProduct(t41, t42, t43, t44, 1, 0, 0, 1); ans[15] = matrixProduct(t41, t42, t43, t44, 1, 0, 0, 0); } } // 3. 計算後の 第0成分(1行1列) を 返却. // for(int i = 0; i < 16; i++) cout << ans[i] << " "; return ans[0]; } int main() { // 1. 入力情報取得. LL Q; cin >> Q; // 2. 各クエリごとに, Tetranacci数列 を 17 で割った余りを出力. for(LL i = 0; i < Q; i++){ LL q; cin >> q; LL t = tetranacciByMatrix(q); cout << t << endl; } // 3. 後処理. return 0; }