Easy Compare-and-Set

문제

Let us define "Compare-and-Set" operation for a global variable $vv$. The operation checks if the variable is equal to $aa$. If that's true, the variable value changes to $bb$ and the operation succeeds. Otherwise, the variable doesn't change and the operation fails. Let us denote the operation as $\mathrm{CAS}(a,b)\backslash operatorname\{CAS\}(a,b)$.

Imagine that you are given a list of such operations $\mathrm{CAS}(a_1,b_1),\dots ,\mathrm{CAS}(a_n,b_n)\backslash operatorname\{CAS\}(a\_1,b\_1),\; \backslash dots,\; \backslash operatorname\{CAS\}(a\_n,b\_n)$. Also, you are given an initial value for the variable, $cc$, and a list of wishes $w_1,\dots w_{n}w\_1,\; \backslash dots\; w\_n$, where $w_{i}w\_i$ tells whether the operation $\mathrm{CAS}(a_i,b_i)\backslash operatorname\{CAS\}(a\_i,b\_i)$ should be successful. Your task is to determine the order of operations execution so that all the wishes are satisfied.

입력

The first line contains two integers $nn$ and $cc$ ($1\le n\le {10}^{5}1\; \backslash le\; n\; \backslash le\; 10^5$; $1\le c\le {10}^{9}1\; \backslash le\; c\; \backslash le\; 10^9$) --- the number of operations and the initial value of the variable.

Each of the next $nn$ lines contains three integers $a_i,b_i,w_{i}a\_i,\; b\_i,\; w\_i$ ($1\le a_i,b_i\le {10}^{9}1\; \backslash le\; a\_i,\; b\_i\; \backslash le\; 10^9$; $0\le w_i\le 10\; \backslash le\; w\_i\; \backslash le\; 1$), denoting $\mathrm{CAS}(a_i,b_i)\backslash operatorname\{CAS\}(a\_i,\; b\_i)$ operation that you wish to be successful if $w_i=1w\_i\; =\; 1$ and unsuccessful if $w_i=0w\_i\; =\; 0$. The operations are numbered from $11$ to $nn$ in order of input.

출력

If no correct order of operations exists, output a single word "No".

Otherwise, output a word "Yes" followed by $nn$ distinct integers $p_1,p_2,\dots p_{n}p\_1,\; p\_2,\; \backslash ldots\; p\_n$ ($1\le p_i\le n1\; \backslash le\; p\_i\; \backslash le\; n$), meaning that operation $p_{1}p\_1$ should be executed first, then operation $p_{2}p\_2$, and so on. If there are several possible orders, output any of them.