Anchal lives in a city which has $N$​ ice cream parlours. The city has $N-1$ connections such that every ice cream parlour can be reached from every other ice cream parlour. Each parlour has only one type of ice cream with cost $C_{i}$​ for each $1 \le i \le N$​. Anchal has $Q$​ queries with each query specifying a city $R$​ and two integers $X$ and $Y$. In every query she wants to reach the same destination ice cream parlour $D$.Anchal wants to calculate the number of cities from which she can start her journey and reach the destination city $D$​ along the shortest path between the source and the destination city such that city $R$ lies in its path and the sum of ice creams for these three cities lie between $X$​ and $Y$ (Both inclusive).

Note : City $D$ , City $R$ and the city from which Anchal starts are pairwise distinct.

INPUT FORMAT

• First line consists of three space separated integers $N$ , $Q$ and $D$ as described above 
• Second line consists of $N$ space separated integers with $i^{th}$ integer denoting $C_{i}$ as described above
• Next $N-1$ lines each consist of 2 space separated integers $U$ and $V$ denoting there is a bidirectional path from ice cream parlour $U$ to $V$ and vice versa
• Each of the following $Q$ lines contain three space separated integers $IN_{1}$ , $IN_{2}$ and $IN_{3}$  describing one query. Lets define $last$ as the answer of the previous query (If its first query then $last$ = 0). The parameters of the query can be calculated by : 
  • $R=IN_{1} \oplus last$
  • $X=IN_{2} \oplus last$
  • $Y=IN_{3} \oplus last$

where ${\oplus}$ is the symbol for logical XOR.

OUTPUT FORMAT

• For each query, print the answer to it on a separate line

CONSTRAINTS

• $1 \le N,Q \le 10^5$
• $1 \le D, R \le N$ and $R \ne D$
• $1 \le X,Y,C_{i} \le 10^{12}$
• $X \le Y$

SUBTASKS

• For 10 Points : $1 \le N,Q \le 100$
• For 20 Points : $1 \le N,Q \le 1000$
• For 70 Points : Original Constraints