Problem: Notice: unusual memory limit!

After the war, destroyed cities in the neutral zone were restored. And children went back to school.

The war changed the world, as well as education. In those hard days, a new math concept was created.

As we all know, logarithm function can be described as: $$$ log(p_1^{a_1}p_2^{a_2}...p_k^{a_2}) = a_1 log p_1 + a_2 log p_2 + ... + a_k log p_k  Where p_1^{a_1}p_2^{a_2}...p_k^{a_2}$$$ is the prime factorization of a integer. A problem is that the function uses itself in the definition. That is why it is hard to calculate.

So, the mathematicians from the neutral zone invented this: $$$ exlog_f(p_1^{a_1}p_2^{a_2}...p_k^{a_2}) = a_1 f(p_1) + a_2 f(p_2) + ... + a_k f(p_k) $$$

Notice that exlog_f(1) is always equal to 0.

This concept for any function f was too hard for children. So teachers told them that f can only be a polynomial of degree no more than 3 in daily uses (i.e., f(x) = Ax^3+Bx^2+Cx+D).

"Class is over! Don't forget to do your homework!" Here it is: $$$ ∑_{i=1}^n exlog_f(i) $$$

Help children to do their homework. Since the value can be very big, you need to find the answer modulo 2^{32}.

Input

The only line contains five integers n, A, B, C, and D (1 ≤ n ≤ 3 ⋅ 10^8, 0 ≤ A,B,C,D ≤ 10^6).

Output

Print the answer modulo 2^{32}.

Examples

Input

12 0 0 1 0


Output

63


Input

4 1 2 3 4


Output

136

Note

In the first sample:

exlog_f(1) = 0

exlog_f(2) = 2

exlog_f(3) = 3

exlog_f(4) = 2 + 2 = 4

exlog_f(5) = 5

exlog_f(6) = 2 + 3 = 5

exlog_f(7) = 7

exlog_f(8) = 2 + 2 + 2 = 6

exlog_f(9) = 3 + 3 = 6

exlog_f(10) = 2 + 5 = 7

exlog_f(11) = 11

exlog_f(12) = 2 + 2 + 3 = 7

 ∑_{i=1}^{12} exlog_f(i)=63 

In the second sample:

exlog_f(1) = 0

exlog_f(2) = (1 × 2^3 + 2 × 2^2 + 3 × 2 + 4) = 26

exlog_f(3) = (1 × 3^3 + 2 × 3^2 + 3 × 3 + 4) = 58

exlog_f(4) = 2 × exlog_f(2) = 52

 ∑_{i=1}^4 exlog_f(i)=0+26+58+52=136 

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScan in = new MyScan(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        long[] abcd;
        long[] vals = new long[1562500];
        private static long _m = (1L << 32) - 1;
        int t = 63;

        public void solve(int testNumber, MyScan in, PrintWriter out) {
            int n = in.nextInt();
            abcd = in.nl(4);

            long ans = 0;
            ans = (ans + getAns(n, 2)) & _m;
            ans = (ans + getAns(n, 3)) & _m;
            for (int l = 1; ; l++) {
                int trans = toi(l);
                if (trans > n) break;
                if (is(l)) continue;
                if (trans < 17_500) {
                    int offset = trans << 1;
                    for (int t = trans * trans; t <= n; t += offset) {
                        set(from(t));
                    }
                }


                ans = (ans + getAns(n, trans)) & _m;
            }
            out.println(ans);
        }

        public boolean is(int f) {
            return (vals[f >> 6] & (1L << (f & t))) != 0;
        }

        public void set(int i) {
            vals[i >> 6] |= 1L << (i & t);
        }

        private long getAns(int n, int s) {
            int curN = n;
            int sum = 0;
            while (curN > 0) {
                curN /= s;
                sum += curN;
            }
            return (sum * f(s)) & _m;
        }

        private long f(int x) {
            long res = 0;
            long m = 1;
            res += (abcd[3] * m) & _m;
            m = m * x;
            res += (abcd[2] * m) & _m;
            m = (m * x) & _m;
            res += (abcd[1] * m) & _m;
            m = (m * x) & _m;
            res += (abcd[0] * m) & _m;
            return res & _m;
        }

        int from(int ind) {
            int s = ind % 6;
            if (s != 1 && s != 5) return 0;
            int ans = ind / 6;
            ans <<= 1;
            if (s == 5) ans++;
            return ans;
        }

        int toi(int ind) {
            int k = (ind >> 1) * 6 + 1;
            if ((ind & 1) == 1) {
                k += 4;
            }
            return k;
        }

    }

    static class MyScan {
        private final InputStream in;
        private byte[] inbuf = new byte[1024];
        public int lenbuf = 0;
        public int ptrbuf = 0;

        public MyScan(InputStream in) {
            this.in = in;
        }

        private int readByte() {
            if (lenbuf == -1) throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = in.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0) return -1;
            }
            return inbuf[ptrbuf++];
        }

        public long[] nl(int n) {
            long[] k = new long[n];
            for (int i = 0; i < n; i++) {
                k[i] = nextLong();
            }
            return k;
        }

        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

    }
}