CodeForces 552C. Vanya and Scales（进制+思维）

C. Vanya and Scales

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Vanya has a scales for weighing loads and weights of masses w0, w1, w2, ..., w100 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.

Input

The first line contains two integers w, m (2 ≤ w ≤ 109, 1 ≤ m ≤ 109) — the number defining the masses of the weights and the mass of the item.

Output

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

Examples

input

3 7

output

YES

input

100 99

output

YES

input

100 50

output

NO

Note

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.

解题思路：将m转化为w进制 以从左往右数 第n位的权值即为w^(n-1) 检索每一位的值是否符合题意 分三种情况

1.该位值为0 则两边不加砝码

2.该位值为1 则在物品另一边增加砝码

3.该位值加1后进位 注意此时下一位的值需是0 否则需要两个下一位的砝码 无法实现 

很早之前写的题 有点忘了 因为当时觉得巧妙就一直记着 作为处女篇吧 ～下面附代码 代码简单 比较需要思考

#include <stdio.h>#include <string.h>int main(){    int n;int m;    scanf("%d%d",&n,&m);    while(m)    {        if(m%n==0||m%n==1)           {               m=m/n;           }        else if(m%n==n-1)        {            m=(m+1)/n;        }        else        {            printf("NO\n");            return 0;        }    }    printf("YES\n");    }