def count_picking_ways(n: int, m: int, a: List[int]) -> List[int]:
    """
    This is the easy version of the problem. The only difference between easy and hard versions is the constraint of $m$. You can make hacks only if both versions are solved.
    
    Chiori loves dolls and now she is going to decorate her bedroom![Image]
    
    As a doll collector, Chiori has got $n$ dolls. The $i$-th doll has a non-negative integer value $a_i$ ($a_i < 2^m$, $m$ is given). Chiori wants to pick some (maybe zero) dolls for the decoration, so there are $2^n$ different picking ways.
    
    Let $x$ be the bitwise-xor-sum of values of dolls Chiori picks (in case Chiori picks no dolls $x = 0$). The value of this picking way is equal to the number of $1$-bits in the binary representation of $x$. More formally, it is also equal to the number of indices $0 \leq i < m$, such that $\left\lfloor \frac{x}{2^i} \right\rfloor$ is odd.
    
    Tell her the number of picking ways with value $i$ for each integer $i$ from $0$ to $m$. Due to the answers can be very huge, print them by modulo $998\,244\,353$.
    
    
    -----Input-----
    
    The first line contains two integers $n$ and $m$ ($1 \le n \le 2 \cdot 10^5$, $0 \le m \le 35$)  — the number of dolls and the maximum value of the picking way.
    
    The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i < 2^m$)  — the values of dolls.
    
    
    -----Output-----
    
    Print $m+1$ integers $p_0, p_1, \ldots, p_m$  — $p_i$ is equal to the number of picking ways with value $i$ by modulo $998\,244\,353$.
    
    
    -----Examples-----
    Input
    4 4
    3 5 8 14
    
    Output
    2 2 6 6 0
    Input
    6 7
    11 45 14 9 19 81
    
    Output
    1 2 11 20 15 10 5 0
    """


# Tests

def check(candidate):
    assert count_picking_ways(4, 4, [3, 5, 8, 14]) == [2, 2, 6, 6, 0]
    assert count_picking_ways(6, 7, [11, 45, 14, 9, 19, 81]) == [1, 2, 11, 20, 15, 10, 5, 0]
    assert count_picking_ways(1, 0, [0]) == [2]
    assert count_picking_ways(30, 35, [11712212162, 13887261936, 9226451478, 5810578422, 4558800999, 2160186631, 25345435752, 20420262166, 16723017889, 4041013095, 17986671533, 30276157972, 27290831854, 10571984774, 24307466845, 32173907391, 15769943440, 28953863917, 1549581104, 13064028174, 1138889079, 12556425529, 26841655665, 18139754266, 5735510830, 3178397383, 7757108363, 15850451442, 11041191850, 17872176930]) == [4, 0, 16, 208, 1672, 9908, 50904, 210400, 734032, 2209780, 5738368, 13028432, 26080504, 46141348, 72492200, 101511648, 126865608, 141776868, 141823824, 126878576, 101475192, 72509020, 46144296, 26068512, 13036528, 5737756, 2208288, 736112, 208904, 50764, 10328, 1568, 244, 12, 0, 0]
    assert count_picking_ways(1, 1, [1]) == [1, 1]
    assert count_picking_ways(1, 35, [0]) == [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
    assert count_picking_ways(1, 35, [11451423333]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
    assert count_picking_ways(10, 34, [0, 0, 12318192370, 9052534583, 0, 4986123150, 184250432, 4986123150, 0, 184250432]) == [64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 128, 64, 192, 128, 128, 128, 0, 64, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
    assert count_picking_ways(35, 35, [28970678337, 13247197766, 4600355530, 18082505493, 16706083720, 2360325080, 23035896777, 30607216979, 32966877835, 32966877835, 18508953859, 8718641292, 16706083720, 8718641292, 28970678337, 29062095447, 31585209157, 29062095447, 18082505493, 24992043025, 32966877835, 28970678337, 24992043025, 24349067783, 4600355530, 16706083720, 12649054530, 26987450767, 29062095447, 13247197766, 22145858015, 2062883350, 10922253140, 30607216979, 2062883350]) == [75497471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75497471, 226492413, 377487355, 452984826, 377487355, 301989884, 226492413, 75497471, 150994942, 0, 0, 0, 0, 75497471, 0, 0, 0, 0, 0, 0, 0, 0, 0]
    assert count_picking_ways(6, 35, [23601314651, 29074846252, 10638992479, 32779777411, 26378409257, 33108582487]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 8, 6, 6, 8, 8, 7, 5, 7, 3, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
    assert count_picking_ways(30, 30, [65536, 536870912, 2097152, 512, 32768, 16384, 8388608, 16777216, 524288, 4194304, 1, 1048576, 2048, 262144, 64, 4096, 8192, 256, 131072, 2, 268435456, 33554432, 32, 16, 134217728, 8, 67108864, 128, 4, 1024]) == [1, 30, 435, 4060, 27405, 142506, 593775, 2035800, 5852925, 14307150, 30045015, 54627300, 86493225, 119759850, 145422675, 155117520, 145422675, 119759850, 86493225, 54627300, 30045015, 14307150, 5852925, 2035800, 593775, 142506, 27405, 4060, 435, 30, 1]
    assert count_picking_ways(30, 30, [16777215, 7, 2097151, 131071, 15, 127, 1073741823, 3, 4095, 536870911, 134217727, 8191, 31, 255, 65535, 511, 8388607, 16383, 4194303, 524287, 1, 32767, 33554431, 1048575, 1023, 63, 262143, 2047, 67108863, 268435455]) == [1, 30, 435, 4060, 27405, 142506, 593775, 2035800, 5852925, 14307150, 30045015, 54627300, 86493225, 119759850, 145422675, 155117520, 145422675, 119759850, 86493225, 54627300, 30045015, 14307150, 5852925, 2035800, 593775, 142506, 27405, 4060, 435, 30, 1]
    assert count_picking_ways(30, 31, [16385, 131072, 67108865, 1073741825, 1048577, 5, 65536, 16, 4096, 32, 33554432, 1024, 536870912, 2097153, 4194304, 3, 32768, 262145, 268435457, 9, 524289, 16777217, 256, 2049, 134217728, 65, 8388608, 128, 512, 8192]) == [1, 16, 225, 2240, 15785, 85008, 367913, 1314560, 3945045, 10080720, 22174581, 42334656, 70562765, 103129040, 132588045, 150266880, 150273315, 132594480, 103124035, 70557760, 42337659, 22177584, 10079355, 3943680, 1315015, 368368, 84903, 15680, 2255, 240, 15, 0]
    assert count_picking_ways(30, 31, [7, 3, 1, 2097151, 511, 31, 1023, 4095, 536870911, 16383, 2047, 268435455, 33554431, 15, 8388607, 131071, 134217727, 67108863, 4194303, 65535, 8191, 1048575, 32767, 16777215, 524287, 1073741823, 63, 262143, 255, 127]) == [1, 30, 435, 4060, 27405, 142506, 593775, 2035800, 5852925, 14307150, 30045015, 54627300, 86493225, 119759850, 145422675, 155117520, 145422675, 119759850, 86493225, 54627300, 30045015, 14307150, 5852925, 2035800, 593775, 142506, 27405, 4060, 435, 30, 1, 0]
    assert count_picking_ways(35, 35, [536870910, 4194303, 8388606, 1023, 131070, 8190, 17179869183, 262143, 510, 16777215, 255, 33554430, 63, 4095, 2147483646, 65535, 6, 15, 8589934590, 524286, 30, 134217726, 16383, 34359738366, 2046, 32766, 126, 2097150, 1048575, 4294967295, 268435455, 67108863, 8589934590, 1073741823, 3]) == [2, 0, 1190, 0, 104720, 0, 3246320, 0, 47071640, 0, 367158792, 0, 670659247, 0, 646941388, 0, 133903076, 0, 90936123, 0, 506420202, 0, 956186894, 0, 834451800, 0, 141214920, 0, 13449040, 0, 649264, 0, 13090, 0, 70, 0]
    assert count_picking_ways(36, 35, [8193, 4194305, 262145, 536870913, 524289, 8589934593, 4294967297, 2147483649, 129, 1048577, 33, 4097, 131073, 2097153, 16777217, 1073741825, 33554433, 65, 1025, 257, 32769, 5, 134217729, 1025, 3, 17179869185, 9, 268435457, 513, 8193, 8388609, 16385, 2049, 67108865, 17, 65537]) == [4, 0, 2380, 0, 209440, 0, 6492640, 0, 94143280, 0, 734317584, 0, 343074141, 0, 295638423, 0, 267806152, 0, 181872246, 0, 14596051, 0, 914129435, 0, 670659247, 0, 282429840, 0, 26898080, 0, 1298528, 0, 26180, 0, 140, 0]
    assert count_picking_ways(36, 35, [16384, 1048576, 2048, 268435456, 8, 256, 65536, 16777216, 128, 33554432, 4294967296, 32768, 1073741824, 4194304, 8388608, 8589934592, 4, 536870912, 2, 512, 131072, 16, 524288, 32768, 8192, 4096, 1, 2097152, 262144, 134217728, 64, 17179869184, 1024, 32, 2147483648, 67108864]) == [2, 70, 1190, 13090, 104720, 649264, 3246320, 13449040, 47071640, 141214920, 367158792, 834451800, 670659247, 956186894, 646941388, 506420202, 133903076, 90936123, 90936123, 133903076, 506420202, 646941388, 956186894, 670659247, 834451800, 367158792, 141214920, 47071640, 13449040, 3246320, 649264, 104720, 13090, 1190, 70, 2]
check(count_picking_ways)