本题只需要先将$x$进制数转换成$10$进制数，然后再从十进制数转换成$y$进制数就可以了。
注意C/C++提交需要高精度
cpp代码

#include <cstdio>
#include <vector>
#include <queue>
#include <cstring>
#include <cmath>
#include <map>
#include <set>
#include <string>
#include <iostream>
#include <algorithm>
#include <iomanip>
using namespace std;
#define sd(n) scanf("%d",&n)
#define sdd(n,m) scanf("%d%d",&n,&m)
#define sddd(n,m,k) scanf("%d%d%d",&n,&m,&k)
#define pd(n) printf("%d\n", n)
#define pc(n) printf("%c", n)
#define pdd(n,m) printf("%d %d", n, m)
#define pld(n) printf("%lld\n", n)
#define pldd(n,m) printf("%lld %lld\n", n, m)
#define sld(n) scanf("%lld",&n)
#define sldd(n,m) scanf("%lld%lld",&n,&m)
#define slddd(n,m,k) scanf("%lld%lld%lld",&n,&m,&k)
#define sf(n) scanf("%lf",&n)
#define sc(n) scanf("%c",&n)
#define sff(n,m) scanf("%lf%lf",&n,&m)
#define sfff(n,m,k) scanf("%lf%lf%lf",&n,&m,&k)
#define ss(str) scanf("%s",str)
#define rep(i,a,n) for(int i=a;i<=n;i++)
#define per(i,a,n) for(int i=n;i>=a;i--)
#define mem(a,n) memset(a, n, sizeof(a))
#define debug(x) cout << #x << ": " << x << endl
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define mod(x) ((x)%MOD)
#define gcd(a,b) __gcd(a,b)
#define lowbit(x) (x&-x)
typedef pair<int,int> PII;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
const int MOD = 1e9 + 7;
const double eps = 1e-9;
const ll INF = 0x3f3f3f3f3f3f3f3fll;
const int inf = 0x3f3f3f3f;
inline int read()
{
    int ret = 0, sgn = 1;
    char ch = getchar();
    while(ch < '0' || ch > '9')
    {
        if(ch == '-')
            sgn = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9')
    {
        ret = ret*10 + ch - '0';
        ch = getchar();
    }
    return ret*sgn;
}
inline void Out(int a)    //ê?3?ía1ò
{
    if(a>9)
        Out(a/10);
    putchar(a%10+'0');
}

int qpow(int m, int k, int mod)
{
    int res = 1, t = m;
    while (k)
    {
        if (k&1)
            res = res * t % mod;
        t = t * t % mod;
        k >>= 1;
    }
    return res;
}

ll gcd(ll a,ll b)
{
    return b==0?a : gcd(b,a%b);
}

ll lcm(ll a,ll b)
{
    return a*b/gcd(a,b);
}
const int maxn = 1000;
int  t[maxn], A[maxn];
char str1[maxn], str2[maxn];
int n, m;
void solve()
{
    int i, len, k;
    len = strlen(str1);
    for(i=len; i>=0; --i)
        t[len-1-i] = str1[i] -(str1[i]<58 ? 48: str1[i]<97 ? 55: 61);
    for(k=0; len;)
    {
        for(i=len; i>=1; --i)
        {
            t[i-1] +=t[i]%m*n;
            t[i] /= m;
        }
        A[k++] = t[0] % m;
        t[0] /=m;
        while(len>0&&!t[len-1])
            len--;
    }
    str2[k] =NULL;
    for(i=0; i<k; i++)
        str2[k-1-i] = A[i]+(A[i]<10 ? 48: A[i]<36 ? 55:61);
}

int main()
{
    scanf("%d%d%s",&n, &m, str1);
    solve();
    printf("%s\n",str2);
    return 0;
}

Java代码

import java.math.BigInteger;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		String z;
		int x,y;
		Scanner input=new Scanner(System.in);
		x=input.nextInt();
		y=input.nextInt();
		z = input.next();
		if(z.equals("0"))
		{
			System.out.println(0);
			return;
		}
		BigInteger big1=Toten(z, x);
		String res=reverse(ToY(big1, y));
		System.out.println(res);
	}
	
	static String reverse(String str)
	{
		String s="";
		int len = str.length();
		for(int i = len-1;i >= 0;i--)
		{
			s+=str.charAt(i);
		}
		return s;
	}
	static String ToY(BigInteger a,int y) {
		String res="";
		BigInteger zero=new BigInteger("0");
		BigInteger ynum=new BigInteger(""+y);
		int tnum;
		while(!a.equals(zero))
		{
			tnum=Integer.valueOf(a.remainder(ynum).toString());
			res+=inttochar(tnum);
			a=a.divide(ynum);
		}
		return res;
	}
	static BigInteger Toten(String str,int x) {
		BigInteger res=new BigInteger("0");
		BigInteger tb;
		BigInteger tBigInteger=BigInteger.ONE;
		BigInteger k = BigInteger.valueOf(x);
		int len = str.length();
		for(int i = len-1; i >= 0;i--){
			tb=new BigInteger(tBigInteger.toString());
			res=res.add(chartoint(str.charAt(i)).multiply(tb));
			tBigInteger = tBigInteger.multiply(k);
		}
		return res;
	}
	static BigInteger chartoint(Character ch)
	{
		int t=0;
		BigInteger bigInteger;
	    if(ch>='0'&&ch<='9') {
	    	t = ch-'0';
	    }
	    else if(ch>='A'&&ch<='Z') {
	    	t = ch-'A'+10;
	    }
	    else if(ch>='a'&&ch<='z') {
	    	t = ch-'a'+36;
	    }
	    bigInteger=new BigInteger(""+t);
	    return bigInteger;
	}
	static Character inttochar(int n)
	{
	    if(n>=0&&n<=9)
	        return (char) ('0'+n);
	    else if(n>=10&&n<=35)
	        return (char) ('A'+n-10);
	    else
	        return (char) ('a'+n-36);
	}
}