Hey guys !!

Hope you all are in good condition and enjoying the lock down (if there's one in your region) :):)

I accidentally stumbled upon a question of trees and online queries which I am unable to solve. I'm attaching the image containing the question. And just in case if it's not clear

You are given a tree with N vertices, rooted at vertex 1 (indexed from 1 to N). Each vertex has a value associated with it. The value of $$$i_{th}$$$ vertex is $$$a_i$$$. Consider $$$f_i$$$ as the $$$a_i$$$ th beauftiful number.

A beautiful number is a number whose sum of squares of digits is less than or equal to X. You have to process M queries where each query can be

Type 1 -> 1 i y : update $$$a-i$$$ to y

Type 2 -> 2 i : output the sum of $$$f_i$$$ for all the nodes in the sub-tree of node i ( including node i). Since the number can be very large compute it modulo 998244353.

CONSTRAINTS :

1 <= N, M, i, $$$u_i$$$, $$$v_i$$$, $$$a_i$$$, y <= 5*$$$10^5$$$

1 <= X <= $$$10^{10}$$$