#!/usr/bin/tclsh
namespace path {::tcl::mathop ::tcl::mathfunc}

proc lsum L {expr [join $L +]+0}
proc random range {expr int(rand()*$range)}

proc genAnsList {n_max lPair lAns} {
 upvar $lPair lPair1
 upvar $lAns lAns1
 set lPair {{0 0}}
 set lPair1 {{0 0}}

 for {set i 1} {[<= $i $n_max]} {incr i} {
  set q [/ [+ [sqrt 5] 1 ] 2]
  set a [int [* $q $i]]
  set b [+ $a $i]
  lappend lPair1 "$a $b"
  lappend lPair "$a $b"
  lappend lPair "$b $a"
 }

 set lPairSorted [lsort -integer -index 0 $lPair]
 for {set i 0} {[<= $i $n_max]} {incr i} {
  lappend lAns1 [lindex [lindex $lPairSorted $i] 1]
 }
}

proc turn {st lAns lPair} {
 set st_cur_sum [lsum $st]
 if {[== 0 $st_cur_sum]} {return {you win}}

 set a [lindex $st 0]
 set b [lindex $st 1]
 set c [abs [- $a $b]]

 set a1 [min $a [lindex $lAns $b]]
 set b1 [min $b [lindex $lAns $a]]
 set cPair1 [lindex $lPair $c]

 set a2 [random $a]
 set b2 [random $b]
 set c2 [random [+ 1 [min $a $b]]]
 set cPair2 [list [- $a $c2] [- $b $c2]]

 set st_next1 [list "$a $b1" [+ $a $b1]]
 set st_next2 [list "$a1 $b" [+ $a1 $b]]
 set st_next3 [list "$cPair1" [lsum $cPair1]]
 set lst_next [list $st_next1 $st_next2 $st_next3]
 set st_next [lindex [lsort -integer -index 1 $lst_next] 0]
 set st_next_sum [lindex $st_next 1]

 if {[== 0 $st_next_sum]} {return {i won}}

 if {[> $st_cur_sum  $st_next_sum]} {
   return [lindex $st_next 0]
 } else {
  switch [random 3] {
   0 {return "$a $b2"}
   1 {return "$a2 $b"}
   2 {return "$cPair2"}
  }
 }
}

puts {Enter heap sizes:}
if {[< 0 [gets stdin state]]} {
 set n_max [lindex [lsort -integer $state] end]
 genAnsList $n_max lPair lAns
 set state [turn $state $lAns $lPair]
 puts $state

 while {[< 0 [gets stdin state]]} {
  set state [turn $state $lAns $lPair]
  puts $state
 }
}