import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.NoSuchElementException; public class Main { final long MOD=(long)1e9+9; int NMAX=100; long[] fac=new long[NMAX]; long[] inv=new long[NMAX]; long[] ifac=new long[NMAX]; { fac[0]=fac[1]=ifac[0]=ifac[1]=inv[0]=inv[1]=1; for (int i=2;i=MOD?a+b-MOD:a+b); } long[] interpolate(long[] a) { long[] f=new long[a.length]; for (int v=0;v