CF2072F Goodbye, Banker Life

Monsters are approaching the city, and to protect it, Akito must create a protective field around the city. As everyone knows, protective fields come in various levels. Akito has chosen the field of level $ n $ . To construct the field, a special phrase is required, which is the $ n $ -th row of the Great Magical Triangle, represented as a two-dimensional array. We will call this array $ T $ . The triangle is defined as follows: - In the $ i $ -th row, there are $ i $ integers. - The single integer in the first row is $ k $ . - Let the $ j $ -th element of the $ i $ -th row be denoted as $ T_{i,j} $ . Then $ $$$T_{i,j} = \begin{cases} T_{i-1,j-1} \oplus T_{i-1,j}, &\textrm{if } 1 < j < i \\ T_{i-1,j}, &\textrm{if } j = 1 \\ T_{i-1,j-1}, &\textrm{if } j = i \end{cases} $ $ where $ a \\oplus b $ is the bitwise exclusive "OR"(XOR) of the integers $ a $ and $ b $ .

Help Akito find the integers in the $ n$$$-th row of the infinite triangle before the monsters reach the city.

The first line contains the integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. In the only line of each test case, there are two integers $ n $ and $ k $ ( $ 1 \le n \le 10^6,\ 1 \le k < 2^{31} $ ) — the row index that Akito needs and the integer in the first row of the Great Magical Triangle, respectively. It is guaranteed that the sum of $ n $ across all test cases does not exceed $ 10^6 $ .

For each test case, output $ n $ integers — the elements of the $ n $ -th row of the Great Magical Triangle.

In the first example, the first row of the Great Magical Triangle is $ [5] $ by definition. In the second example, $ T_{2,1} = T_{1,1} = 10 $ and $ T_{2,2} = T_{1, 1} = 10 $ .