import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main1 {

	public static void main(String[] args) throws Throwable {
		Scanner sc = new Scanner(System.in);
		int k = sc.nextInt() , b = sc.nextInt() , n = sc.nextInt() , t = sc.nextInt();
		int ans = n;
		if(k!=1)
			for(int i = n-1; i>=0 && Math.pow(k, n-i)-(1e-7)<=1l*(t*(k-1l)+b)/(k-1l+b);--i,--ans);
		else
			for(int i = n-1;i>=0 && 1l*b*n+1l<=1l*b*i + 1l*t;--i,--ans);
		System.out.println(ans);
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(String file) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public int[] nexIntArray() throws Throwable {
			st = new StringTokenizer(br.readLine());
			int[] a = new int[st.countTokens()];
			for (int i = 0; i < a.length; i++)
				a[i] = nextInt();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}

}
