private static long pow ( long a , long n ) {
  if ( n == 0 ) return 1 ;
  long ans = pow ( a , n / 2 ) ;
  ans *= ans ;
  ans %= mod ;
  if ( n % 2 == 1 ) {
    ans *= a ;
    ans %= mod ;
  }
  return ans ;
}

private static long pow ( long a , long n ) { if ( n == 0 ) return 1 ; long ans = pow ( a , n / 2 ) ; ans *= ans ; ans %= mod ; if ( n % 2 == 1 ) { ans *= a ; ans %= mod ; } return ans ; }
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