import math from bisect import bisect_left, bisect_right from typing import Generic, Iterable, Iterator, List, Tuple, TypeVar, Optional T = TypeVar('T') class SortedMultiset(Generic[T]): BUCKET_RATIO = 16 SPLIT_RATIO = 24 def __init__(self, a: Iterable[T] = []) -> None: "Make a new SortedMultiset from iterable. / O(N) if sorted / O(N log N)" a = list(a) n = self.size = len(a) if any(a[i] > a[i + 1] for i in range(n - 1)): a.sort() bucket_size = int(math.ceil(math.sqrt(n / self.BUCKET_RATIO))) self.a = [a[n * i // bucket_size : n * (i + 1) // bucket_size] for i in range(bucket_size)] def __iter__(self) -> Iterator[T]: for i in self.a: for j in i: yield j def __reversed__(self) -> Iterator[T]: for i in reversed(self.a): for j in reversed(i): yield j def __eq__(self, other) -> bool: return list(self) == list(other) def __len__(self) -> int: return self.size def __repr__(self) -> str: return "SortedMultiset" + str(self.a) def __str__(self) -> str: s = str(list(self)) return "{" + s[1 : len(s) - 1] + "}" def _position(self, x: T) -> Tuple[List[T], int, int]: "return the bucket, index of the bucket and position in which x should be. self must not be empty." for i, a in enumerate(self.a): if x <= a[-1]: break return (a, i, bisect_left(a, x)) def __contains__(self, x: T) -> bool: if self.size == 0: return False a, _, i = self._position(x) return i != len(a) and a[i] == x def count(self, x: T) -> int: "Count the number of x." return self.index_right(x) - self.index(x) def add(self, x: T) -> None: "Add an element. / O(√N)" if self.size == 0: self.a = [[x]] self.size = 1 return a, b, i = self._position(x) a.insert(i, x) self.size += 1 if len(a) > len(self.a) * self.SPLIT_RATIO: mid = len(a) >> 1 self.a[b:b+1] = [a[:mid], a[mid:]] def _pop(self, a: List[T], b: int, i: int) -> T: ans = a.pop(i) self.size -= 1 if not a: del self.a[b] return ans def discard(self, x: T) -> bool: "Remove an element and return True if removed. / O(√N)" if self.size == 0: return False a, b, i = self._position(x) if i == len(a) or a[i] != x: return False self._pop(a, b, i) return True def lt(self, x: T) -> Optional[T]: "Find the largest element < x, or None if it doesn't exist." for a in reversed(self.a): if a[0] < x: return a[bisect_left(a, x) - 1] def le(self, x: T) -> Optional[T]: "Find the largest element <= x, or None if it doesn't exist." for a in reversed(self.a): if a[0] <= x: return a[bisect_right(a, x) - 1] def gt(self, x: T) -> Optional[T]: "Find the smallest element > x, or None if it doesn't exist." for a in self.a: if a[-1] > x: return a[bisect_right(a, x)] def ge(self, x: T) -> Optional[T]: "Find the smallest element >= x, or None if it doesn't exist." for a in self.a: if a[-1] >= x: return a[bisect_left(a, x)] def __getitem__(self, i: int) -> T: "Return the i-th element." if i < 0: for a in reversed(self.a): i += len(a) if i >= 0: return a[i] else: for a in self.a: if i < len(a): return a[i] i -= len(a) raise IndexError def pop(self, i: int = -1) -> T: "Pop and return the i-th element." if i < 0: for b, a in enumerate(reversed(self.a)): i += len(a) if i >= 0: return self._pop(a, ~b, i) else: for b, a in enumerate(self.a): if i < len(a): return self._pop(a, b, i) i -= len(a) raise IndexError def bisect(self, x: T) -> int: "Count the number of elements < x." ans = 0 for a in self.a: if a[-1] >= x: return ans + bisect_left(a, x) ans += len(a) return ans def index_right(self, x: T) -> int: "Count the number of elements <= x." ans = 0 for a in self.a: if a[-1] > x: return ans + bisect_right(a, x) ans += len(a) return ans def mul(A,B): l,m,n = len(A),len(B),len(B[0]) C = [[0] * n for i in range(l)] for i in range(l): for j in range(m): a = A[i][j] for k in range(n): C[i][k] = (C[i][k] + a * B[j][k]) % mod return C def Mul(A,B): C = [[0 for i in range(3)] for j in range(3)] for i in range(3): for j in range(3): for k in range(3): C[i][k] += B[i][j] * A[j][k] C[i][k] %= mod return C class segtree(): n=1 size=1 log=2 d=[0] op=None e=10**15 def __init__(self,V,OP,E): self.n=len(V) self.op=OP self.e=E self.log=(self.n-1).bit_length() self.size=1<>i) def get(self,p): assert 0<=p and p>=1 r>>=1 return self.op(sml,smr) def all_prod(self): return self.d[1] def max_right(self,l,f): assert 0<=l and l<=self.n assert f(self.e) if l==self.n: return self.n l+=self.size sm=self.e while(1): while(l%2==0): l>>=1 if not(f(self.op(sm,self.d[l]))): while(l1 and (r%2)): r>>=1 if not(f(self.op(self.d[r],sm))): while(r= r: break X.append(p) P.discard(p) for x in X: seg.set(x,E) else: D = seg.prod(l,r) dp = mul(D,[[0],[0],[1]]) print((dp[0][0] + dp[1][0]) % mod)