U500139 Unmelted Snow

[Chinese Statement](https://www.luogu.com.cn/problem/P11245). **You must submit your code at the Chinese version of the statement.**  As if in a dream, by the telescope that had been with her for so long, Yun found a little boy.「If you please — draw me an ocean......」 --- **The Little Prince**: Wow! How do you know me? Are you looking for your star too? **Yun**: Uh, but, I've been on this star since birth. **The Little Prince**: Then why — why do you like looking at them? **Yun**: Because they remind me of the infinite possibilities: every star could be a whole new world. **The Little Prince** *(ponders for a moment)*: Do the stars also send messages to each other? I suppose you are fascinated by the message... And in what way would they communicate? **Yun**: If the stars were to communicate with each other, I guess it would probably be through signals, perhaps simple symbols like $\tt 0$ and $\tt 1$. **The Little Prince**: You're kind of like those grown-ups —「I'm crunching these cumbersome numbers」— that's what they'd always say. I might prefer these to $\tt 0$ and $\tt 1$: peaks and troughs, they remind me of an ocean: where I come from, there is no ocean, but my rose used to talk to me about it, which she wanted me to hold her in my arms and look at together ......

**Yun**: My guess is that, if the stars wanted to talk, they would speak a series of「signals」of length $n + m$ — a『wave』consisting of $n$ peaks and $m$ troughs. Unfortunately, what the stars say sometimes doesn't reach very far ......    —— This is because of『black holes』. A signal from a star can pass through a black hole of width $[L, R]$ and subsequently reach far away, if and only if, there are no continuous sub-wave in it that can be absorbed by the black hole. For certain $L, R$, a continuous sub-wave can be absorbed, if and only if: - its length is an even number between $[2L, 2R]$; - Let its length be $2k$, then it contains **exactly** $k$ peaks and $k$ troughs.    I often liked to look at the stars, and I recorded all their words as waves. Unfortunately, sometimes I couldn't draw such a big ocean, even though that star far away was actually minute in my eyes. Facing the overwhelming variety, I could only write down a sequence of integers $n, m, L, R$. And yet my memories still went wrong from time to time.    Flipping through the $q$ lines of notes I once had, I wonder,「If the star were to send me a message in the form of a wave of $n$ peaks and $m$ troughs, would it still be possible for me to receive the original message after it passes through a black hole of width $[L, R]$?」— That is, **is there a wave with $\bm n$ peaks and $\bm m$ troughs in which no continuous sub-wave can be absorbed by a black hole of width $\bm{[L, R]}$?**     After all, the excitement of picking up the telescope so long ago has finally faded away, leaving me with only the most succinct and coldest fragments at hand. I think this is also a kind of submission to the rules of the adults. *But before that, Yun still wanted to solve those questions she left behind. So, she gave you her notes.*

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For convenience, *we* still denote $\tt 0$ as the peak and $\tt 1$ as the trough. - In the first sample test case, because there are both $\tt 0, 1$ but $L = 1$, it must be illegal. - In the second sample test case, you can construct the wave as $\tt 0011111100$. - In the third sample test case, such is the fact. - For other sample test cases, no clear responce will be given temporarily. --- **The Little Prince**: If it weren't for these annoying numbers — it seems like an interesting problem that I would figure out. So, how will grown-ups on your planet solve it? Do they also use the so-called $n, m, L, R$ as well as $\tt 0$ and $\tt 1$? **Yun** *(smiling)*: Adults may see this as a complex mathematical problem or need to draw many charts to calculate. However, sometimes they forget that as long as there is a rose in the heart, the answer is no longer difficult to get. **The Little Prince** *(sighs softly)*: Yes, many things are not actually complicated, while they just see them so.