One night, The King of Involuted King of Rainbow Island had just finished study and was going back to his dormitory. But a strange thing happened. Every street lamp went out. But because he studied day and night, God gave him a magic to light all the street lamps numbered $[1, L]$. Of course it would be easy to light them one by one, but as the King of Involuted King, he didn't want to do that. So he generates $n$ intervals for himself, and then randomly selects from $n$ options with equal probability (can be repeatedly selected), asks what is the expectation of lighting all the streetlights. If can not light all lights output $-1$.
Senior warm tip: being a involuted king is a good thing, but also to pay attention to the body health, but still should try to play more codeforces!
输入格式
Each test contains multiple test cases. The first line contains the number of test cases $T$ ($1 \leq T \leq 200$). Description of the test cases follows.
The first line of each test contains two numbers, $n(1\leq n\leq 10)$ and $L(1\leq L\leq 10^9)$, indicating the number of intervals and the number of streetlights.
The next $n$ lines, each containing two digits $l$ and $r$, represent the interval $[l,r]$.$(1\leq l_i,r_i\leq L)$.
输出格式
For each test, output expected value.
It can be proved that the expected value is always a rational number. Additionally, under the constraints of this problem, when that value is represented as $Q/P$ using two coprime integers $P$ and $Q$，it can be proved that there uniquely exists an integer $R$ such that $R\times Q\equiv P(mod \ 998244353)$ and $0\leq R < 998244353$. In this case, you should find this $R$.
