static long inv ( long a , long mod ) {
  long b = mod ;
  long p = 1 , q = 0 ;
  while ( b > 0 ) {
    long c = a / b ;
    long d = a ;
    a = b ;
    b = d % b ;
    d = p ;
    p = q ;
    q = d - c * q ;
  }
  return ( mod + p ) % mod ;
}

static long inv ( long a , long mod ) { long b = mod ; long p = 1 , q = 0 ; while ( b > 0 ) { long c = a / b ; long d = a ; a = b ; b = d % b ; d = p ; p = q ; q = d - c * q ; } return ( mod + p ) % mod ; }
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