static long modInv ( long a ) {
  long p = MOD - 2 ;
  long s = 1 ;
  while ( p != 1 ) {
    if ( p % 2 == 1 ) s = ( s * a ) % MOD ;
    a = ( a * a ) % MOD ;
    p /= 2 ;
  }
  return ( a * s ) % MOD ;
}

static long modInv ( long a ) { long p = MOD - 2 ; long s = 1 ; while ( p != 1 ) { if ( p % 2 == 1 ) s = ( s * a ) % MOD ; a = ( a * a ) % MOD ; p /= 2 ; } return ( a * s ) % MOD ; }
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