Vanya has a scales for weighing loads and weights of masses $w^0, w^1, w^2, \dots, w^{100}$ grams where $w$ is some integer not less than $2$ (exactly one weight of each nominal value). Vanya wonders whether he can weight an item with mass $m$ using the given weights, if the weights can be put on both pans of the scales. Formally speaking, your task is to determine whether it is possible to place an item of mass $m$ and some weights on the left pan of the scales, and some weights on the right pan of the scales so that the pans of the scales were in balance. --- 你有 $101$ 个砝码，质量分别为 $w^0, w^1, w^2, \dots, w^{100}$ 克，其中 $w$ 为一个不小于 $2$ 的整数。 问能否通过这些砝码，在天平上称量出质量恰好为 $m$ 的物体？ 砝码可以与物体放在同一侧，也可以放在另一侧。

The first line contains two integers $w, m$ $(2 \le w \le 10^9, 1 \le m \le 10^9)$ — the number defining the masses of the weights and the mass of the item.

Print word `YES` if the item can be weighted and `NO` if it cannot.

Note to the first sample test. One pan can have an item of mass $7$ and a weight of mass $3$, and the second pan can have two weights of masses $9$ and $1$, correspondingly. Then $7 + 3 = 9 + 1$. Note to the second sample test. One pan of the scales can have an item of mass $99$ and the weight of mass $1$, and the second pan can have the weight of mass $100$. Note to the third sample test. It is impossible to measure the weight of the item in the manner described in the input.

Codeforces Div. 2 [CF552C] | 第二届ACC(AcWing Cup)全国联赛