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#8694. 魔法字符串

统计

考虑字符串序列 $F_1, F_2, \dots$,定义如下:

$$F_1 = ab$$ $$F_{k+1} = F_k F_k b$$

计算字符串 $F_n$ 的不同子序列个数,结果对 $10^9 + 7$ 取模。

输入格式

第一行包含一个整数 $t$ ($1 \le t \le 10$),表示测试用例的数量。 第二行包含 $t$ 个整数 $n$ ($1 \le n \le 10^{18}$),每个测试用例对应一个 $n$。

输出格式

对于每个测试用例,输出一个整数作为问题的答案。连续的答案之间用空格隔开。

样例

样例输入 1

3
1 2 3

样例输出 1

4 17 226

说明

前三个字符串为:$F_1 = ab$,$F_2 = ababb$,以及 $F_3 = ababbababbb$。

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