import math class SegTree: DEFAULT = { 'min': 1 << 60, 'max': -(1 << 60), 'sum': 0, 'prd': 1, 'gcd': 0, 'lmc': 1, '^': 0, '&': (1 << 60) - 1, '|': 0, } FUNC = { 'min': min, 'max': max, 'sum': (lambda x, y: x + y), 'prd': (lambda x, y: x * y), 'gcd': math.gcd, 'lmc': (lambda x, y: (x * y) // math.gcd(x, y)), '^': (lambda x, y: x ^ y), '&': (lambda x, y: x & y), '|': (lambda x, y: x | y), } def __init__(self, ls, mode='min', func=None, default=None): """ 要素ls, 関数mode (min,max,sum,prd(product),gcd,lmc,^,&,|) func,defaultを指定すれば任意の関数、単位元での計算が可能 """ N = len(ls) if default == None: self.default = self.DEFAULT[mode] else: self.default = default if func == None: self.func = self.FUNC[mode] else: self.func = func self.N = N self.K = (N - 1).bit_length() self.N2 = 1 << self.K self.dat = [self.default] * (2**(self.K + 1)) for i in range(self.N): # 葉の構築 self.dat[self.N2 + i] = ls[i] self.build() def build(self): for j in range(self.N2 - 1, -1, -1): self.dat[j] = self.func(self.dat[j << 1], self.dat[j << 1 | 1]) # 親が持つ条件 def leafvalue(self, x): # リストのx番目の値 return self.dat[x + self.N2] def update(self, x, y): # index(x)をyに変更 i = x + self.N2 self.dat[i] = y while i > 0: # 親の値を変更 i >>= 1 self.dat[i] = self.func(self.dat[i << 1], self.dat[i << 1 | 1]) return def query(self, L, R): # [L,R)の区間取得 L += self.N2 R += self.N2 vL = self.default vR = self.default while L < R: if L & 1: vL = self.func(vL, self.dat[L]) L += 1 if R & 1: R -= 1 vR = self.func(self.dat[R], vR) L >>= 1 R >>= 1 return self.func(vL, vR) def __iter__(self): for i in range(self.N): yield self[i] def __getitem__(self, x): return self.leafvalue(x) if (type(x) is int) else self.query(x[0],x[1]) def __setitem__(self, x, val): return self.update(x, val) class Node: def __init__(self,default): self.rch = None self.lch = None self.val = default class PersistentSegTree: def __init__(self, ls): setnum = list(set(ls[:])) setnum.sort() self.dic_num_ID = dict() self.dic_ID_num = dict() for i,v in enumerate(setnum): self.dic_ID_num[i] = v self.dic_num_ID[v] = i ls = [self.dic_num_ID[i] for i in ls] self.N0 = len(ls) N = len(setnum) self.default = 0 self.func = (lambda x, y: x + y) self.N = N self.K = (N - 1).bit_length() self.N2 = 1 << self.K self.dat = [Node(0) for _ in range(2**(self.K + 1))] self.build() self.verdict = dict() self.verdict[-1] = 1 for i in range(self.N0): self.update_x_val_told_tnew(ls[i],self.leafvalue_t(ls[i],i-1)+1,i-1,i) def build(self): for node in range(self.N2 - 1, 0, -1): self.dat[node].rch = self.dat[node<<1 | 1] self.dat[node].lch = self.dat[node<<1] self.dat[node].val = self.func(self.dat[node<<1 | 1].val,self.dat[node<<1].val) self.dat.pop() self.dat.pop() def leafvalue_t(self, x, t): # ver.tにおけるリストのx番目の値 ''' version:tにおけるindex:xの値を出力 ''' x += self.N2 v = self.dat[self.verdict[t]] # ver.tの根 path = bin(x)[3:] for i in path: if i == '0': v = v.lch else: v = v.rch return v.val def update_x_val_told_tnew(self,x,val,told,tnew): # logN ''' x: 変更するindex val: 変更後の値 told: 変更前のversion tnew: 変更後のversion ''' x += self.N2 path = bin(x)[3:] self.verdict[tnew] = len(self.dat) new_nodes = [Node(self.default) for _ in range(len(path)+1)] v_old = self.dat[self.verdict[told]] v_new = new_nodes[0] now = 1 for i in path: # ノードをつなげる if i == '0': v_new.rch = v_old.rch v_new.lch = new_nodes[now] v_new = new_nodes[now] v_old = v_old.lch else: v_new.lch = v_old.lch v_new.rch = new_nodes[now] v_new = new_nodes[now] v_old = v_old.rch now += 1 v_new.val = val for node in range(len(path)-1,-1,-1): # 付け加えたノードの値を子から親に更新 new_nodes[node].val = self.func(new_nodes[node].lch.val,new_nodes[node].rch.val) self.dat.append(new_nodes[0]) def get_all_t(self,t): # NlogN ''' version:tにおける配列を出力 return : list ''' ret = [] for i in range(self.N2,self.N2+self.N): path = bin(i)[3:] v = self.dat[self.verdict[t]] for p in path: if p == '0': v = v.lch else: v = v.rch ret.append(v.val) return ret def kth_query(self, L, R, k): # ver.tにおける[L,R)のクエリ ''' 区間kthクエリ[L,R) 区間[L,R)でk番目に大きい数を出力 kは0オリジン ''' k += 1 if k > (R-L): return None vl = self.dat[self.verdict[L-1]] vr = self.dat[self.verdict[R-1]] path = 1 cnt = 0 while True: cntnow = cnt + vr.lch.val - vl.lch.val if cntnow < k: cnt += vr.lch.val-vl.lch.val path = (path << 1) | 1 vl = vl.rch vr = vr.rch else: path = (path << 1) vl = vl.lch vr = vr.lch if vl.lch == None: break path -= self.N2 return self.dic_ID_num[path] import collections N, Q = map(int,input().split()) lsA = list(map(int,input().split())) dic_num_ls = collections.defaultdict(lambda:[]) for i in range(N): dic_num_ls[lsA[i]].append(i) SG = PersistentSegTree(lsA) lsLRmid = [] for i in range(Q): #(L,R,mid,i) [L,R)で持つ L,R = map(int,input().split()) L -= 1 mid = SG.kth_query(L,R,(R-L)//2) lsLRmid.append((L,R,mid,i)) lsLRmid.sort(key=lambda x:x[2]) lsLRnew = [] md = 0 keys = list(dic_num_ls.keys()) keys.sort() SGsum = SegTree([0]*N,mode='sum') SGcnt = SegTree([0]*N,mode='sum') for key in keys: for j in dic_num_ls[key]: SGsum.update(j,key) SGcnt.update(j,1) while md