#1153054 (PyPy3) No.3478 XOR-Folding Primes

• 問題: No.3478 XOR-Folding Primes
• ユーザー: lif4635
• 提出日時: 2026-03-20 21:54:46
• 言語: PyPy3 (7.3.17)
• 結果: AC
• 実行時間: 2,328 ms / 4,000 ms
• コード長: 5,143 bytes
• コンパイル時間: 283 ms
• コンパイル使用メモリ: 85,216 KB
• 実行使用メモリ: 270,696 KB
• 最終ジャッジ日時: 2026-03-20 21:55:05
• 合計ジャッジ時間: 14,580 ms
• ジャッジサーバーID （参考情報）: judge2_0 / judge1_1

ファイルパターン	結果
sample	AC * 1
other	AC * 8

ソースコード

# input
import sys
input = sys.stdin.readline
II = lambda : int(input())
MI = lambda : map(int, input().split())
LI = lambda : [int(a) for a in input().split()]
SI = lambda : input().rstrip()
LLI = lambda n : [[int(a) for a in input().split()] for _ in range(n)]
LSI = lambda n : [input().rstrip() for _ in range(n)]
MI_1 = lambda : map(lambda x:int(x)-1, input().split())
LI_1 = lambda : [int(a)-1 for a in input().split()]

mod = 998244353
inf = 1001001001001001001
ordalp = lambda s : ord(s)-65 if s.isupper() else ord(s)-97
ordallalp = lambda s : ord(s)-39 if s.isupper() else ord(s)-97
yes = lambda : print("Yes")
no = lambda : print("No")
yn = lambda flag : print("Yes" if flag else "No")

prinf = lambda ans : print(ans if ans < 1000001001001001001 else -1)
alplow = "abcdefghijklmnopqrstuvwxyz"
alpup = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
alpall = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
URDL = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)}
DIR_4 = [[-1,0],[0,1],[1,0],[0,-1]]
DIR_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]]
DIR_BISHOP = [[-1,1],[1,1],[1,-1],[-1,-1]]
prime60 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59]
sys.set_int_max_str_digits(0)
# sys.setrecursionlimit(10**6)
# import pypyjit
# pypyjit.set_param('max_unroll_recursion=-1')

from collections import defaultdict,deque
from heapq import heappop,heappush
from bisect import bisect_left,bisect_right
DD = defaultdict
BSL = bisect_left
BSR = bisect_right

class Comb:
    __slots__ = ["fac", "finv", "mod"]
    def __init__(self, lim:int, mod:int = mod):
        """
        mod : prime
        """
        self.fac = [1]*(lim+1)
        self.finv = [1]*(lim+1)
        self.mod = mod
        for i in range(2,lim+1):
            self.fac[i] = self.fac[i-1]*i%self.mod
        self.finv[lim] = pow(self.fac[lim],-1,mod)
        for i in range(lim,2,-1):
            self.finv[i-1] = self.finv[i]*i%self.mod
    
    def C(self, a, b):
        if b < 0 or a < b: return 0
        if a < 0: return 0
        return self.fac[a]*self.finv[b]%self.mod*self.finv[a-b]%self.mod
    
    def __call__(self, a, b):
        if b < 0 or a < b: return 0
        if a < 0: return 0
        return self.fac[a]*self.finv[b]%self.mod*self.finv[a-b]%self.mod
    
    def P(self, a, b):
        if b < 0 or a < b: return 0
        if a < 0: return 0
        return self.fac[a]*self.finv[a-b]%self.mod
    
    def M(self, *k):
        n = sum(k)
        if n < 0: return 0
        res = self.fac[n]
        for ki in k:
            if ki < 0: return 0
            res = res * self.finv[ki] % self.mod
        return res
    
    def H(self, a, b): return self.C(a+b-1,b)
    def F(self, a): return self.fac[a]
    def Fi(self, a): return self.finv[a]

def prime_enumerate(lim:int, get:int = 0) -> list[int]:
    """
    get = 0 : enumerate
    get = 1 : flag
    """
    lim += 1
    prime_flag = [1]*lim
    prime_enu = []
    prime_flag[0] = 0
    prime_flag[1] = 0
    for p in range(2,lim):
        if prime_flag[p]:
            prime_enu.append(p)
            for q in range(2*p,lim,p):
                prime_flag[q] = 0
    if get == 0:
        return prime_enu
    else:
        return prime_flag  

mod = 998244353

def mat_add(a, b):
    # assert len(a) == len(b)
    # assert len(a[0]) == len(b[0])
    n = len(a)
    m = len(a[0])
    res = [[0]*m for i in range(n)]
    for i in range(n):
        for j in range(m):
            res[i][j] = (a[i][j] + b[i][j])%mod
    return res

def mat_sub(a, b):
    # assert len(a) == len(b)
    # assert len(a[0]) == len(b[0])
    n = len(a)
    m = len(a[0])
    res = [[0]*m for i in range(n)]
    for i in range(n):
        for j in range(m):
            res[i][j] = (a[i][j] - b[i][j])%mod
    return res

def mat_mul(a, b):
    # assert len(a[0]) == len(b)
    n = len(a)
    m = len(b[0])
    res = [[0]*m for i in range(n)]
    for i,r_i in enumerate(res):
        for k,a_ik in enumerate(a[i]):
            for j,b_kj in enumerate(b[k]):
                r_i[j] = (r_i[j] + a_ik*b_kj)%mod
    return res

def mat_pow2(a):
    n = len(a)
    res = [[0]*n for i in range(n)]
    for i,r_i in enumerate(res):
        for k,a_ik in enumerate(a[i]):
            for j,a_kj in enumerate(a[k]):
                r_i[j] = (r_i[j] + a_ik*a_kj)%mod
    return res

def mat_inv(a, mod = mod):
    """いつか実装します"""
    pass

def mat_pow(a, exp):
    n = len(a)
    res = [[int(i == j) for j in range(n)] for i in range(n)]
    
    d = exp.bit_length()
    for i in range(d, -1, -1):
        if (exp >> i) & 1: res = mat_mul(res, a)
        if i == 0: return res
        res = mat_pow2(res)

ps = prime_enumerate(10 ** 7 + 1)
comb = Comb(10 ** 7 + 1)

# ^ 2 素数の数え上げ

ok = []
for i in range(len(ps) - 1):
    if ps[i]^2 == ps[i+1]:
        ok.append(ps[i+1])

def solve():
    n, m = MI()
    if n == 1:
        print(bisect_right(ps, m))
        return
    
    c = bisect_right(ok, m)
    # p -> 2 or 
    m = [[0, 1], [2 * c, 1]]
    r = mat_pow(m, n - 1)
    ans = r[0][0] + r[1][0] + (r[0][1] + r[1][1]) * (2 * c) 
    print(ans % mod)

t = II()
for i in range(t):
    solve()