Vanya and Jackets

Vanya wants to change his life again and plans which jacket to wear over the next $n$ days. He owns $m$ jackets. Jacket $i$ can be worn at temperatures from $l_i$ to $r_i$, inclusive. The forecast gives temperature $a_j$ for day $j$. On day $j$, he must wear a jacket $i$ such that $l_i \le a_j \le r_i$. He never wears the same jacket on two consecutive days. His mother does not allow him to leave home without a jacket or to wear more than one, so every day needs exactly one jacket. Build a schedule that satisfies all of these rules.

The first line contains two integers $n$ and $m$ ($1 \le n, m \le 100000$), the number of days and the number of jackets. The second line contains $n$ integers $a_1, a_2, ..., a_n$ ($0 \le a_i \le 10^9$), the temperature on each day. Then $m$ lines follow. The $i$-th of them contains two integers $l_i$ and $r_i$ ($0 \le l_i \le r_i \le 10^9$), the temperature range of the $i$-th jacket.

If a valid schedule exists, print Yes on the first line. On the second line, print $n$ integers $b_1, b_2, ..., b_n$, where $b_i$ is the index of the jacket worn on day $i$. Jackets are numbered from 1 in input order. Otherwise, print No. If several schedules are valid, print any of them.

In the first sample, the answer 2 1 2 4 is not the only correct one. Another correct answer is 1 2 1 4. In the second sample, no valid schedule exists because the first jacket is the only option for both day 1 and day 2.