Containers and Reagents

Peter got a new task from his chemistry teacher. He has to pour reagents into containers. There are $n$ containers and $m$ reagents.

Container $i$ carries two constraints. The total volume of liquid in it must be at least $\min_i$ milliliters and at most $\max_i$ milliliters, and reagent $c_i$ must occupy at least $p_i$ percent of the liquid volume in it.

Peter has $v_i$ milliliters of reagent $i$. Every reagent must be poured into containers completely, and every container must hold at least one reagent. A poured amount does not have to be an integer. No chemical reaction happens and no volume changes.

Decide whether Peter can pour everything so that all constraints hold.

For example, suppose there are 3 containers and 4 reagents, the container constraints are $(\min, \max, c, p) = (5, 8, 1, 60), (4, 6, 3, 80), (3, 4, 4, 70)$ in this order, and the available reagent volumes are $3, 4, 4, 3$. Pour 3 milliliters of reagent 1 and 2 milliliters of reagent 2 into container 1, 4 milliliters of reagent 3 and 1 milliliter of reagent 2 into container 2, and 3 milliliters of reagent 4 and 1 milliliter of reagent 2 into container 3. The volumes are 5, 5 and 4 milliliters, all inside their ranges, and the percentages are $3/5 = 60\%$, $4/5 = 80\%$ and $3/4 = 75\% \ge 70\%$. Every reagent is used up, so the answer here is YES.

The input contains several test cases. The first line holds the number of test cases $t$ ($1 \le t \le 100$).

The first line of each test case holds the number of containers $n$ and the number of reagents $m$ ($1 \le n, m \le 10^5$).

The $i$-th of the next $n$ lines holds four integers $\min_i$, $\max_i$, $c_i$, $p_i$ ($1 \le \min_i \le \max_i \le 10^5$, $1 \le c_i \le m$, $1 \le p_i \le 100$): the minimum volume of liquid in container $i$, its maximum volume, the number of the reagent that carries the percentage constraint there, and the minimum percentage that reagent must occupy.

The next line holds the integers $v_1, v_2, \dots, v_m$ ($1 \le v_i \le 10^5$).

The sum of $n$ and the sum of $m$ over all test cases in one input each do not exceed $10^5$.

For each test case print the answer on its own line. Print YES if the reagents can be poured so that all constraints hold, and NO otherwise. Print both words in upper case.