; LLVM IR from ShahjalalShohag/code-library :: Math (NTT Online (D&C))

; Unoptimized IR (clang -disable-llvm-passes):
target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
target triple = "x86_64-unknown-linux-gnu"

%"class.std::basic_istream" = type { ptr, i64, %"class.std::basic_ios" }
%"class.std::basic_ios" = type { %"class.std::ios_base", ptr, i8, i8, ptr, ptr, ptr, ptr }
%"class.std::ios_base" = type { ptr, i64, i64, i32, i32, i32, ptr, %"struct.std::ios_base::_Words", [8 x %"struct.std::ios_base::_Words"], i32, ptr, %"class.std::locale" }
%"struct.std::ios_base::_Words" = type { ptr, i64 }
%"class.std::locale" = type { ptr }
%"class.std::basic_ostream" = type { ptr, %"class.std::basic_ios" }

@ans = external dso_local global [100009 x i32], align 16
@a = external dso_local global [100009 x i32], align 16
@dp = external dso_local global [100009 x i32], align 16
@_ZSt3cin = external global %"class.std::basic_istream", align 8
@_ZSt4cout = external global %"class.std::basic_ostream", align 8

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #0

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #0

; Function Attrs: mustprogress nounwind uwtable
declare dso_local void @_Z3prev() #1

; Function Attrs: mustprogress nounwind uwtable
declare dso_local noundef i32 @_Z7catalani(i32 noundef) #1

; Function Attrs: mustprogress uwtable
declare dso_local void @_Z2yoii(i32 noundef, i32 noundef) #2

; Function Attrs: mustprogress norecurse uwtable
define dso_local noundef i32 @main() #3 {
  %1 = alloca i32, align 4
  %2 = alloca i32, align 4
  %3 = alloca i32, align 4
  %4 = alloca i32, align 4
  %5 = alloca i32, align 4
  store i32 0, ptr %1, align 4
  call void @_Z3prev()
  call void @llvm.lifetime.start.p0(i64 4, ptr %2) #7
  call void @llvm.lifetime.start.p0(i64 4, ptr %3) #7
  %6 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16) @_ZSt3cin, ptr noundef nonnull align 4 dereferenceable(4) %2)
  %7 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16) %6, ptr noundef nonnull align 4 dereferenceable(4) %3)
  call void @llvm.lifetime.start.p0(i64 4, ptr %4) #7
  %8 = load i32, ptr %2, align 4, !tbaa !5
  %9 = sdiv i32 %8, 2
  store i32 %9, ptr %4, align 4, !tbaa !5
  %10 = call noundef nonnull align 4 dereferenceable(4) ptr @_ZSt3minIiERKT_S2_S2_(ptr noundef nonnull align 4 dereferenceable(4) %3, ptr noundef nonnull align 4 dereferenceable(4) %4)
  %11 = load i32, ptr %10, align 4, !tbaa !5
  store i32 %11, ptr %3, align 4, !tbaa !5
  call void @llvm.lifetime.end.p0(i64 4, ptr %4) #7
  call void @llvm.lifetime.start.p0(i64 4, ptr %5) #7
  store i32 1, ptr %5, align 4, !tbaa !5
  br label %12

12:                                               ; preds = %33, %0
  %13 = load i32, ptr %5, align 4, !tbaa !5
  %14 = load i32, ptr %3, align 4, !tbaa !5
  %15 = mul nsw i32 2, %14
  %16 = icmp sle i32 %13, %15
  br i1 %16, label %18, label %17

17:                                               ; preds = %12
  call void @llvm.lifetime.end.p0(i64 4, ptr %5) #7
  br label %36

18:                                               ; preds = %12
  %19 = load i32, ptr %5, align 4, !tbaa !5
  %20 = and i32 %19, 1
  %21 = icmp ne i32 %20, 0
  br i1 %21, label %22, label %23

22:                                               ; preds = %18
  br label %28

23:                                               ; preds = %18
  %24 = load i32, ptr %5, align 4, !tbaa !5
  %25 = sdiv i32 %24, 2
  %26 = sub nsw i32 %25, 1
  %27 = call noundef i32 @_Z7catalani(i32 noundef %26)
  br label %28

28:                                               ; preds = %23, %22
  %29 = phi i32 [ 0, %22 ], [ %27, %23 ]
  %30 = load i32, ptr %5, align 4, !tbaa !5
  %31 = sext i32 %30 to i64
  %32 = getelementptr inbounds [100009 x i32], ptr @a, i64 0, i64 %31
  store i32 %29, ptr %32, align 4, !tbaa !5
  br label %33

33:                                               ; preds = %28
  %34 = load i32, ptr %5, align 4, !tbaa !5
  %35 = add nsw i32 %34, 1
  store i32 %35, ptr %5, align 4, !tbaa !5
  br label %12, !llvm.loop !9

36:                                               ; preds = %17
  store i32 1, ptr @ans, align 16, !tbaa !5
  %37 = load i32, ptr %2, align 4, !tbaa !5
  call void @_Z2yoii(i32 noundef 0, i32 noundef %37)
  %38 = load i32, ptr %2, align 4, !tbaa !5
  %39 = sext i32 %38 to i64
  %40 = getelementptr inbounds [100009 x i32], ptr @dp, i64 0, i64 %39
  %41 = load i32, ptr %40, align 4, !tbaa !5
  %42 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, i32 noundef %41)
  %43 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8) %42, i8 noundef signext 10)
  call void @llvm.lifetime.end.p0(i64 4, ptr %3) #7
  call void @llvm.lifetime.end.p0(i64 4, ptr %2) #7
  ret i32 0
}

declare noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 4 dereferenceable(4)) #4

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef nonnull align 4 dereferenceable(4) ptr @_ZSt3minIiERKT_S2_S2_(ptr noundef nonnull align 4 dereferenceable(4), ptr noundef nonnull align 4 dereferenceable(4)) #5

; Function Attrs: inlinehint mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8), i8 noundef signext) #6

declare noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8), i32 noundef) #4

attributes #0 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #1 = { mustprogress nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #2 = { mustprogress uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #3 = { mustprogress norecurse uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #4 = { "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #5 = { inlinehint mustprogress nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #6 = { inlinehint mustprogress uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #7 = { nounwind }

!llvm.module.flags = !{!0, !1, !2, !3}
!llvm.ident = !{!4}

!0 = !{i32 1, !"wchar_size", i32 4}
!1 = !{i32 8, !"PIC Level", i32 2}
!2 = !{i32 7, !"PIE Level", i32 2}
!3 = !{i32 7, !"uwtable", i32 2}
!4 = !{!"clang version 19.1.0 (git@github.com:llvm/llvm-project.git a4bf6cd7cfb1a1421ba92bca9d017b49936c55e4)"}
!5 = !{!6, !6, i64 0}
!6 = !{!"int", !7, i64 0}
!7 = !{!"omnipotent char", !8, i64 0}
!8 = !{!"Simple C++ TBAA"}
!9 = distinct !{!9, !10}
!10 = !{!"llvm.loop.mustprogress"}


; Optimized IR (opt -passes='default<O3>'):
target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
target triple = "x86_64-unknown-linux-gnu"

%"class.std::basic_istream" = type { ptr, i64, %"class.std::basic_ios" }
%"class.std::basic_ios" = type { %"class.std::ios_base", ptr, i8, i8, ptr, ptr, ptr, ptr }
%"class.std::ios_base" = type { ptr, i64, i64, i32, i32, i32, ptr, %"struct.std::ios_base::_Words", [8 x %"struct.std::ios_base::_Words"], i32, ptr, %"class.std::locale" }
%"struct.std::ios_base::_Words" = type { ptr, i64 }
%"class.std::locale" = type { ptr }
%"class.std::basic_ostream" = type { ptr, %"class.std::basic_ios" }

@ans = external dso_local local_unnamed_addr global [100009 x i32], align 16
@a = external dso_local local_unnamed_addr global [100009 x i32], align 16
@dp = external dso_local local_unnamed_addr global [100009 x i32], align 16
@_ZSt3cin = external global %"class.std::basic_istream", align 8
@_ZSt4cout = external global %"class.std::basic_ostream", align 8

; Function Attrs: mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #0

; Function Attrs: mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #0

; Function Attrs: mustprogress nounwind uwtable
declare dso_local void @_Z3prev() local_unnamed_addr #1

; Function Attrs: mustprogress nounwind uwtable
declare dso_local noundef i32 @_Z7catalani(i32 noundef) local_unnamed_addr #1

; Function Attrs: mustprogress uwtable
declare dso_local void @_Z2yoii(i32 noundef, i32 noundef) local_unnamed_addr #2

; Function Attrs: mustprogress norecurse uwtable
define dso_local noundef i32 @main() local_unnamed_addr #3 {
  %1 = alloca i32, align 4
  %2 = alloca i32, align 4
  %3 = alloca i32, align 4
  tail call void @_Z3prev()
  call void @llvm.lifetime.start.p0(i64 4, ptr nonnull %1) #7
  call void @llvm.lifetime.start.p0(i64 4, ptr nonnull %2) #7
  %4 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16) @_ZSt3cin, ptr noundef nonnull align 4 dereferenceable(4) %1)
  %5 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16) %4, ptr noundef nonnull align 4 dereferenceable(4) %2)
  call void @llvm.lifetime.start.p0(i64 4, ptr nonnull %3) #7
  %6 = load i32, ptr %1, align 4, !tbaa !5
  %7 = sdiv i32 %6, 2
  store i32 %7, ptr %3, align 4, !tbaa !5
  %8 = call noundef nonnull align 4 dereferenceable(4) ptr @_ZSt3minIiERKT_S2_S2_(ptr noundef nonnull align 4 dereferenceable(4) %2, ptr noundef nonnull align 4 dereferenceable(4) %3)
  %9 = load i32, ptr %8, align 4, !tbaa !5
  store i32 %9, ptr %2, align 4, !tbaa !5
  call void @llvm.lifetime.end.p0(i64 4, ptr nonnull %3) #7
  %.not6 = icmp slt i32 %9, 1
  br i1 %.not6, label %._crit_edge, label %.lr.ph

._crit_edge:                                      ; preds = %24, %0
  store i32 1, ptr @ans, align 16, !tbaa !5
  %10 = load i32, ptr %1, align 4, !tbaa !5
  call void @_Z2yoii(i32 noundef 0, i32 noundef %10)
  %11 = load i32, ptr %1, align 4, !tbaa !5
  %12 = sext i32 %11 to i64
  %13 = getelementptr inbounds [100009 x i32], ptr @dp, i64 0, i64 %12
  %14 = load i32, ptr %13, align 4, !tbaa !5
  %15 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, i32 noundef %14)
  %16 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8) %15, i8 noundef signext 10)
  call void @llvm.lifetime.end.p0(i64 4, ptr nonnull %2) #7
  call void @llvm.lifetime.end.p0(i64 4, ptr nonnull %1) #7
  ret i32 0

.lr.ph:                                           ; preds = %0, %24
  %17 = phi i32 [ %25, %24 ], [ %9, %0 ]
  %indvars.iv = phi i64 [ %indvars.iv.next, %24 ], [ 1, %0 ]
  %18 = trunc nuw nsw i64 %indvars.iv to i32
  %19 = and i32 %18, 1
  %.not5 = icmp eq i32 %19, 0
  br i1 %.not5, label %20, label %24

20:                                               ; preds = %.lr.ph
  %21 = lshr exact i32 %18, 1
  %22 = add nsw i32 %21, -1
  %23 = call noundef i32 @_Z7catalani(i32 noundef %22)
  %.pre = load i32, ptr %2, align 4, !tbaa !5
  br label %24

24:                                               ; preds = %.lr.ph, %20
  %25 = phi i32 [ %.pre, %20 ], [ %17, %.lr.ph ]
  %26 = phi i32 [ %23, %20 ], [ 0, %.lr.ph ]
  %27 = getelementptr inbounds [100009 x i32], ptr @a, i64 0, i64 %indvars.iv
  store i32 %26, ptr %27, align 4, !tbaa !5
  %indvars.iv.next = add nuw nsw i64 %indvars.iv, 1
  %28 = shl nsw i32 %25, 1
  %29 = sext i32 %28 to i64
  %.not.not = icmp slt i64 %indvars.iv, %29
  br i1 %.not.not, label %.lr.ph, label %._crit_edge, !llvm.loop !9
}

declare noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 4 dereferenceable(4)) local_unnamed_addr #4

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef nonnull align 4 dereferenceable(4) ptr @_ZSt3minIiERKT_S2_S2_(ptr noundef nonnull align 4 dereferenceable(4), ptr noundef nonnull align 4 dereferenceable(4)) local_unnamed_addr #5

; Function Attrs: inlinehint mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8), i8 noundef signext) local_unnamed_addr #6

declare noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8), i32 noundef) local_unnamed_addr #4

attributes #0 = { mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #1 = { mustprogress nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #2 = { mustprogress uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #3 = { mustprogress norecurse uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #4 = { "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #5 = { inlinehint mustprogress nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #6 = { inlinehint mustprogress uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #7 = { nounwind }

!llvm.module.flags = !{!0, !1, !2, !3}
!llvm.ident = !{!4}

!0 = !{i32 1, !"wchar_size", i32 4}
!1 = !{i32 8, !"PIC Level", i32 2}
!2 = !{i32 7, !"PIE Level", i32 2}
!3 = !{i32 7, !"uwtable", i32 2}
!4 = !{!"clang version 19.1.0 (git@github.com:llvm/llvm-project.git a4bf6cd7cfb1a1421ba92bca9d017b49936c55e4)"}
!5 = !{!6, !6, i64 0}
!6 = !{!"int", !7, i64 0}
!7 = !{!"omnipotent char", !8, i64 0}
!8 = !{!"Simple C++ TBAA"}
!9 = distinct !{!9, !10}
!10 = !{!"llvm.loop.mustprogress"}


; Effective O3 passes: GVNPass,GlobalOptPass,IndVarSimplifyPass,InferFunctionAttrsPass,InstCombinePass,JumpThreadingPass,LoopRotatePass,LoopSimplifyPass,LoopUnrollPass,SROAPass,SimplifyCFGPass,TailCallElimPass