Ural 1104. Don’t Ask Woman about Her Age

1104. Don’t Ask Woman about Her Age

Time limit: 1.0 second

Memory limit: 64 MB

Mrs Little likes digits most of all. Every year she tries to make the best number of the year. She tries to become more and more intelligent and every year studies a new digit. And the number she makes
is written in numeric system which base equals to her age. To make her life more beautiful she writes only numbers that are divisible by her age minus one. Mrs Little wants to hold her age in secret.

You are given a number consisting of digits 0, …, 9 and Latin letters A, …, Z, where A equals 10, B equals 11 etc. Your task is to find the minimal number k satisfying the following condition:
the given number, written in k-based system is divisible by k−1.

Input

Input consists of one string containing no more than 106 digits or uppercase Latin letters.

Output

Output the only number k, or "No solution." if for all 2 ≤ k ≤ 36 condition written above can't be satisfied. By the way, you should write your answer in decimal system.

Sample

input	output
A1A	22

Problem Author: Igor Goldberg

Problem Source: Tetrahedron Team Contest May 2001

/*
N = An*k^(n-1) + An-1*k^(n-2)+……+A0*k^0
k mod (k-1) = 1   N mod（k-1) == An+An-1+……A0 mod （k-1）
*/

#include <iostream>
#include <stdio.h>
#include <string.h>
using namespace std;
char  s[1000010];
int main()
{
    int i, ans, len;
	char c = '/';
	scanf("%s", s);
	ans = 0; len = strlen(s);
	for(i = 0; i < len; i ++) 
	{
		if(s[i] > c) c = s[i];
		if('0'<=s[i]&&s[i]<='9') ans += s[i]-'0';
		else ans += s[i]-'A'+10;
	}
	if(c <= '9') i = c - '0';
	else i = c-'A'+10;
	i ++; if(i < 2) i = 2;
    for(; i <= 36; i ++)
        if(ans%(i-1) == 0) break;
    if(i > 36) printf("No solution.\n");
    else printf("%d\n", i);
    return 0;
}