Packing Biscuits

문제

Aunty Khong is organising a competition with $xx$ participants, and wants to give each participant a bag of biscuits. There are $kk$ different types of biscuits, numbered from $00$ to $k-1k-1$. Each biscuit of type $ii$ ($0\le i\le k-10\; \backslash leq\; i\; \backslash leq\; k-1$) has a tastiness value of $2^{i}2^i$^. Aunty Khong has $a[i]a[i]$ (possibly zero) biscuits of type $ii$ in her pantry.

Each of Aunty Khong's bags will contain zero or more biscuits of each type. The total number of biscuits of type $ii$ in all the bags must not exceed $a[i]a[i]$. The sum of tastiness values of all biscuits in a bag is called the total tastiness of the bag.

Help Aunty Khong find out how many different values of $yy$ exist, such that it is possible to pack $xx$ bags of biscuits, each having total tastiness equal to $yy$.