A13820 | Bubble Cup hypothesis
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内存限制256MB
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题目描述
The Bubble Cup hypothesis stood unsolved for $130$ years. Who ever proves the hypothesis will be regarded as one of the greatest mathematicians of our time! A famous mathematician Jerry Mao managed to reduce the hypothesis to this problem:
Given a number $m$ , how many polynomials $P$ with coefficients in set ${\{0,1,2,3,4,5,6,7\}}$ have: $P(2)=m$ ?
Help Jerry Mao solve the long standing problem!
Given a number $m$ , how many polynomials $P$ with coefficients in set ${\{0,1,2,3,4,5,6,7\}}$ have: $P(2)=m$ ?
Help Jerry Mao solve the long standing problem!
输入格式
The first line contains a single integer $t$ $(1 \leq t \leq 5\cdot 10^5)$ - number of test cases.
On next line there are $t$ numbers, $m_i$ $(1 \leq m_i \leq 10^{18})$ - meaning that in case $i$ you should solve for number $m_i$ .
On next line there are $t$ numbers, $m_i$ $(1 \leq m_i \leq 10^{18})$ - meaning that in case $i$ you should solve for number $m_i$ .
输出格式
For each test case $i$ , print the answer on separate lines: number of polynomials $P$ as described in statement such that $P(2)=m_i$ , modulo $10^9 + 7$ .
输入输出样例
输入 #1
2 2 4
输出 #1
2 4
In first case, for $m=2$ , polynomials that satisfy the constraint are $x$ and $2$ .
In second case, for $m=4$ , polynomials that satisfy the constraint are $x^2$ , $x + 2$ , $2x$ and $4$ .
In second case, for $m=4$ , polynomials that satisfy the constraint are $x^2$ , $x + 2$ , $2x$ and $4$ .
C++ 编辑器
输入
输出
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评测结果：Accepted