Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [46, 9, 31, 27, 88, 13, 10, -22, 58, 86]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    stk = []
    for x in list_1:
        if x > 0:
            stk.append(x)
        else:
            while stk and stk[-1] > 0 and (stk[-1] < -x):
                stk.pop()
            if stk and stk[-1] == -x:
                stk.pop()
            elif not stk or stk[-1] < 0:
                stk.append(x)
    python_result_1 = stk
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-69, -60, -31, 14, 97, -87, -38, 79, 100, 19]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    n = len(list_2)
    ans = 0
    for k in range(1, n + 1):
        t = 0
        j = 1
        while k * j * j <= n:
            t += list_2[k * j * j - 1]
            j += 1
        ans = max(ans, t)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-81, -92, -27, 69, 72, 65, 15, -69, -97, 42]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 19}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_y_static = 6.
Define task_1_bound_static = 22.
Trace the execution of task_1 with inputs y = task_1_y_static, bound = task_1_bound_static.
```python
from typing import List
def task_1(val_1: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_1 == 1:
            break
        a *= val_1
    python_result_1 = list(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [74, -79, 50, 10, 97, -37, -2, 24, 25, 86]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    n = len(list_2)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_2):
        while stk and list_2[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_2[i]
        while stk and list_2[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_2):
        if i and x >= list_2[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_2[i] >= list_2[i + 1]:
            g[i] = g[i + 1] + list_2[i]
        else:
            j = right[i]
            g[i] = list_2[i] * (j - i) + (g[j] if j != n else 0)
    python_result_2 = max((a + b - c for (a, b, c) in zip(f, g, list_2)))
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [39, 76, -39, -16, -64, -27, -78, 8, 5, 17]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -20}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_arr_static = [-11, 39, 17, 91, -79, 81, -10, -68, -42, -61].
Trace the execution of task_1 with inputs arr = task_1_arr_static.
```python
from typing import List
def task_1(arr: List[int], val_1: int) -> int:
    if arr[0] > val_1:
        python_result_1 = val_1
        return python_result_1
    (left, right) = (0, len(arr))
    while left < right:
        mid = left + right >> 1
        if arr[mid] - mid - 1 >= val_1:
            right = mid
        else:
            left = mid + 1
    python_result_1 = arr[left - 1] + val_1 - (arr[left - 1] - (left - 1) - 1)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-33, -50, -40, 49, 3, 70, -14, 14, 63, -13]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_initialEnergy_static = 47.
Define task_2_initialExperience_static = 86.
Define task_2_experience_static = [-7, 94, 74, -17, 10, -49, 77, 77, 86, 11].
Trace the execution of task_2 with inputs initialEnergy = task_2_initialEnergy_static, initialExperience = task_2_initialExperience_static, experience = task_2_experience_static.
```python
from typing import List
def task_2(initialEnergy: int, initialExperience: int, list_2: List[int], experience: List[int]) -> int:
    sum_energy = sum(list_2)
    energy_hours = max(0, sum_energy + 1 - initialEnergy)
    exp_hours = 0
    current_exp = initialExperience
    for e in experience:
        if current_exp <= e:
            delta = e + 1 - current_exp
            exp_hours += delta
            current_exp += delta
        current_exp += e
    python_result_2 = energy_hours + exp_hours
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [67, 67, 17, -5, 7, -50, -59, 22, -22, -15]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -33}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [-5, 48, 45, 8, 10, 57, -72, -33, -73, -9].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> int:
    mx = max(nums)
    n = len(nums)
    ans = cnt = j = 0
    for x in nums:
        while j < n and cnt < val_1:
            cnt += nums[j] == mx
            j += 1
        if cnt < val_1:
            break
        ans += n - j + 1
        cnt -= x == mx
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-88, 41, -97, 7, 38, -78, -83, 66, 16, 88]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_capacityA_static = -9.
Define task_2_capacityB_static = -41.
Trace the execution of task_2 with inputs capacityA = task_2_capacityA_static, capacityB = task_2_capacityB_static.
```python
from typing import List
def task_2(list_2: List[int], capacityA: int, capacityB: int) -> int:
    (a, b) = (capacityA, capacityB)
    ans = 0
    (i, j) = (0, len(list_2) - 1)
    while i < j:
        if a < list_2[i]:
            ans += 1
            a = capacityA
        a -= list_2[i]
        if b < list_2[j]:
            ans += 1
            b = capacityB
        b -= list_2[j]
        (i, j) = (i + 1, j - 1)
    ans += i == j and max(a, b) < list_2[i]
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [80, 24, 84, -21, 70, 3, -47, 17, 42, 87]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [82, 13, -33, 80, 71, -98, -68, 32, -68, -88]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    n = len(list_1)
    stk = []
    left = [-1] * n
    right = [n] * n
    for (i, h) in enumerate(list_1):
        while stk and list_1[stk[-1]] >= h:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    for i in range(n - 1, -1, -1):
        h = list_1[i]
        while stk and list_1[stk[-1]] >= h:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    python_result_1 = max((h * (right[i] - left[i] - 1) for (i, h) in enumerate(list_1)))
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -58}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [-71, -100, -92, 99, 96, 97, -85, 48, 18, 15].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> int:
    nums.sort()
    n = len(nums)
    m = n >> 1
    ans = abs(nums[m] - val_2)
    if nums[m] > val_2:
        for i in range(m - 1, -1, -1):
            if nums[i] <= val_2:
                break
            ans += nums[i] - val_2
    else:
        for i in range(m + 1, n):
            if nums[i] >= val_2:
                break
            ans += val_2 - nums[i]
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [73, 18, -72, 46, -31, 37, 47, 70, -27, -27]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [37, 35, 69, 98, 60, -46, 84, -50, 100, 3]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Define task_1_initialEnergy_static = -6.
Define task_1_initialExperience_static = 68.
Define task_1_experience_static = [60, -82, 82, -74, -6, 25, 28, 17, -72, 12].
Trace the execution of task_1 with inputs initialEnergy = task_1_initialEnergy_static, initialExperience = task_1_initialExperience_static, experience = task_1_experience_static.
```python
from typing import List
def task_1(initialEnergy: int, initialExperience: int, list_1: List[int], experience: List[int]) -> int:
    sum_energy = sum(list_1)
    energy_hours = max(0, sum_energy + 1 - initialEnergy)
    exp_hours = 0
    current_exp = initialExperience
    for e in experience:
        if current_exp <= e:
            delta = e + 1 - current_exp
            exp_hours += delta
            current_exp += delta
        current_exp += e
    python_result_1 = energy_hours + exp_hours
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-40, -59, -72, -67, 14, 36, -32, 15, 77, 6]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    def reverse(arr, j):
        i = 0
        while i < j:
            (arr[i], arr[j]) = (arr[j], arr[i])
            (i, j) = (i + 1, j - 1)
    n = len(list_2)
    ans = []
    for i in range(n - 1, 0, -1):
        j = i
        while j > 0 and list_2[j] != i + 1:
            j -= 1
        if j < i:
            if j > 0:
                ans.append(j + 1)
                reverse(list_2, j)
            ans.append(i + 1)
            reverse(list_2, i)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [33, 88, 21, -21, -22, 21, -64, 32, 81, -64]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 52}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_y_static = 85.
Define task_1_bound_static = 76.
Trace the execution of task_1 with inputs y = task_1_y_static, bound = task_1_bound_static.
```python
from typing import List
def task_1(val_1: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_1 == 1:
            break
        a *= val_1
    python_result_1 = list(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -28}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = 35.
Define task_2_bound_static = 63.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [36, -17, -25, 21, 79, 1, -77, 5, -76, -44]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -99}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_y_static = -98.
Define task_1_bound_static = 17.
Trace the execution of task_1 with inputs y = task_1_y_static, bound = task_1_bound_static.
```python
from typing import List
def task_1(val_1: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_1 == 1:
            break
        a *= val_1
    python_result_1 = list(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -62}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = 84.
Define task_2_bound_static = 64.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [89, 44, 93, -18, 15, -51, 100, -39, -79, -19]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [75, -14, -55, 55, 7, -13, -79, -69, -92, -63]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Define task_1_k_static = -58.
Trace the execution of task_1 with inputs k = task_1_k_static.
```python
from typing import List
def task_1(list_1: List[int], k: int) -> int:
    s = mx_pre = mi_pre = mx_sub = 0
    for x in list_1:
        s += x
        mx_pre = max(mx_pre, s)
        mi_pre = min(mi_pre, s)
        mx_sub = max(mx_sub, s - mi_pre)
    ans = mx_sub
    mod = 10 ** 9 + 7
    if k == 1:
        python_result_1 = ans % mod
        return python_result_1
    mx_suf = s - mi_pre
    ans = max(ans, mx_pre + mx_suf)
    if s > 0:
        ans = max(ans, (k - 2) * s + mx_pre + mx_suf)
    python_result_1 = ans % mod
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 84}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [-69, -51, -38, 93, 67, 3, -97, -44, 55, -77].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-53, 10, 24, 42, -82, -32, 69, -54, 96, 15]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 47}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_y_static = 7.
Define task_1_bound_static = 61.
Trace the execution of task_1 with inputs y = task_1_y_static, bound = task_1_bound_static.
```python
from typing import List
def task_1(val_1: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_1 == 1:
            break
        a *= val_1
    python_result_1 = list(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -10}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [-20, 45, 81, 22, -6, 35, -55, 99, -45, -53].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> int:
    (ans, y) = (1, nums[0])
    for x in nums[1:]:
        if x == 0:
            python_result_2 = 1
            return python_result_2
        if x * y <= val_2:
            y *= x
        else:
            y = x
            ans += 1
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-71, 8, -8, -45, -98, -30, -51, 75, -67, -53]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [44, 38, 9, -34, 45, -33, -86, 6, -27, 79]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    ans = [0, 0]
    n = len(list_1)
    for i in range(2):
        for j in range(i, n, 2):
            d = 0
            if j:
                d = max(d, list_1[j] - list_1[j - 1] + 1)
            if j < n - 1:
                d = max(d, list_1[j] - list_1[j + 1] + 1)
            ans[i] += d
    python_result_1 = min(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -11}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = 61.
Define task_2_bound_static = 80.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [28, -89, -36, 92, -19, 47, -98, 34, -91, -73]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [8, 54, 28, 70, -56, -39, 11, -79, -37, -43]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    k = 3
    n = len(list_1)
    ans = cnt = 0
    for i in range(n << 1):
        if i and list_1[i % n] == list_1[(i - 1) % n]:
            cnt = 1
        else:
            cnt += 1
        ans += i >= n and cnt >= k
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -1}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [-21, 40, -25, -1, 60, 26, 97, -15, 54, 70].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [29, -66, -4, 87, 66, 66, 90, -16, -32, 99]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -57}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [43, -10, -80, -60, -66, 23, 84, -3, 87, 46].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [53, -53, -24, 8, -86, 64, -38, -67, -45, 14]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_queries_static = [-66, 75, -25, 8, -59, -39, 66, -12, 74, 37].
Trace the execution of task_2 with inputs queries = task_2_queries_static.
```python
from typing import List
def task_2(list_2: List[int], queries: List[int]) -> List[int]:
    s = set()
    ans = []
    for q in queries[::-1]:
        if q not in s:
            ans.append(q)
            s.add(q)
    for w in list_2:
        if w not in s:
            ans.append(w)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-67, -41, 12, 8, -24, -72, 93, 74, -65, -61]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_3):
        while stk and list_3[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_3[i]
        while stk and list_3[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_3):
        if i and x >= list_3[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_3[i] >= list_3[i + 1]:
            g[i] = g[i + 1] + list_3[i]
        else:
            j = right[i]
            g[i] = list_3[i] * (j - i) + (g[j] if j != n else 0)
    python_result_3 = max((a + b - c for (a, b, c) in zip(f, g, list_3)))
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [19, 66, -81, -80, -85, -87, 37, 37, -63, 91]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    def reverse(arr, j):
        i = 0
        while i < j:
            (arr[i], arr[j]) = (arr[j], arr[i])
            (i, j) = (i + 1, j - 1)
    n = len(list_1)
    ans = []
    for i in range(n - 1, 0, -1):
        j = i
        while j > 0 and list_1[j] != i + 1:
            j -= 1
        if j < i:
            if j > 0:
                ans.append(j + 1)
                reverse(list_1, j)
            ans.append(i + 1)
            reverse(list_1, i)
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-98, 59, 6, 96, 84, 43, 64, 8, 84, 19]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    n = len(list_2)
    ans = 0
    for k in range(1, n + 1):
        t = 0
        j = 1
        while k * j * j <= n:
            t += list_2[k * j * j - 1]
            j += 1
        ans = max(ans, t)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [89, 82, -95, -82, 31, -30, 33, -73, 77, -2]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-57, -77, 45, -86, 59, 45, -22, 50, -82, 52]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Define task_1_s_static = [37, -60, 56, -38, 8, -31, -17, -4, 36, 83].
Trace the execution of task_1 with inputs s = task_1_s_static.
```python
from typing import List
def task_1(list_1: List[int], s: List[int]) -> int:
    list_1.sort()
    s.sort()
    j = 0
    for (i, x) in enumerate(list_1):
        while j < len(s) and s[j] < list_1[i]:
            j += 1
        if j >= len(s):
            python_result_1 = i
            return python_result_1
        j += 1
    python_result_1 = len(list_1)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [58, 70, -66, 19, -4, -81, -14, 10, 28, -62]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    stk = []
    for x in list_2:
        if x > 0:
            stk.append(x)
        else:
            while stk and stk[-1] > 0 and (stk[-1] < -x):
                stk.pop()
            if stk and stk[-1] == -x:
                stk.pop()
            elif not stk or stk[-1] < 0:
                stk.append(x)
    python_result_2 = stk
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [73, -55, -45, -3, -59, -27, 33, 79, -44, 95]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 86}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_plants_static = [-67, 58, -29, 97, 37, -91, 17, -56, 31, 6].
Define task_1_capacityB_static = -63.
Trace the execution of task_1 with inputs plants = task_1_plants_static, capacityB = task_1_capacityB_static.
```python
from typing import List
def task_1(plants: List[int], val_1: int, capacityB: int) -> int:
    (a, b) = (val_1, capacityB)
    ans = 0
    (i, j) = (0, len(plants) - 1)
    while i < j:
        if a < plants[i]:
            ans += 1
            a = val_1
        a -= plants[i]
        if b < plants[j]:
            ans += 1
            b = capacityB
        b -= plants[j]
        (i, j) = (i + 1, j - 1)
    ans += i == j and max(a, b) < plants[i]
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 71}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_skills_static = [-83, -23, -89, 8, -10, 49, 45, 12, 50, 70].
Trace the execution of task_2 with inputs skills = task_2_skills_static.
```python
from typing import List
def task_2(skills: List[int], val_2: int) -> int:
    n = len(skills)
    val_2 = min(val_2, n - 1)
    i = cnt = 0
    for j in range(1, n):
        if skills[i] < skills[j]:
            i = j
            cnt = 1
        else:
            cnt += 1
        if cnt == val_2:
            break
    python_result_2 = i
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [55, 37, 36, -17, -2, 28, -24, 87, -8, -40]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [39, -70, -40, -19, -3, 79, -69, 84, -10, 89]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Define task_1_k_static = -76.
Trace the execution of task_1 with inputs k = task_1_k_static.
```python
from typing import List
def task_1(list_1: List[int], k: int) -> int:
    if list_1[0] > k:
        python_result_1 = k
        return python_result_1
    (left, right) = (0, len(list_1))
    while left < right:
        mid = left + right >> 1
        if list_1[mid] - mid - 1 >= k:
            right = mid
        else:
            left = mid + 1
    python_result_1 = list_1[left - 1] + k - (list_1[left - 1] - (left - 1) - 1)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 56}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [1, -43, -92, -75, 37, 86, 82, 69, 67, -54].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [55, -84, -56, 26, -81, -14, 29, 14, 11, -85]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 72}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_plants_static = [-1, 16, 8, 70, -25, -79, 61, -21, -37, 26].
Define task_1_capacityB_static = -1.
Trace the execution of task_1 with inputs plants = task_1_plants_static, capacityB = task_1_capacityB_static.
```python
from typing import List
def task_1(plants: List[int], val_1: int, capacityB: int) -> int:
    (a, b) = (val_1, capacityB)
    ans = 0
    (i, j) = (0, len(plants) - 1)
    while i < j:
        if a < plants[i]:
            ans += 1
            a = val_1
        a -= plants[i]
        if b < plants[j]:
            ans += 1
            b = capacityB
        b -= plants[j]
        (i, j) = (i + 1, j - 1)
    ans += i == j and max(a, b) < plants[i]
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 19}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = 57.
Define task_2_bound_static = 56.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-75, -87, 48, -91, 85, -74, -38, 87, 61, -53]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 45}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [-87, 32, -26, 2, 60, -72, 30, -45, -64, -48].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-17, 17, -55, -78, -3, 42, 73, -79, -50, -99]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    nums = [v - i for (i, v) in enumerate(list_2)]
    n = len(nums)
    left = [-1] * n
    stk = []
    for (i, v) in enumerate(nums):
        while stk and nums[stk[-1]] >= v:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    ans = 0
    dp = [0] * n
    dp[0] = list_2[0]
    for (i, v) in enumerate(list_2):
        j = left[i]
        cnt = min(v, i - j)
        u = v - cnt + 1
        s = (u + v) * cnt // 2
        dp[i] = s + (0 if j == -1 else dp[j])
        ans = max(ans, dp[i])
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-15, -61, -80, 24, -83, -26, 29, -17, -54, -55]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-63, -55, -89, 69, 40, 82, 94, -61, -79, -5]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    n = len(list_1)
    ans = [-1] * n
    stk = []
    for i in range(n * 2 - 1, -1, -1):
        i %= n
        while stk and stk[-1] <= list_1[i]:
            stk.pop()
        if stk:
            ans[i] = stk[-1]
        stk.append(list_1[i])
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 68}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [22, 87, -33, 78, 60, -67, -7, 45, -10, 34].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [79, -97, -3, -2, -78, 76, 78, -98, -4, 86]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -74}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_plants_static = [-21, 63, -30, -90, -34, 26, 52, 82, 99, -73].
Define task_1_capacityB_static = 7.
Trace the execution of task_1 with inputs plants = task_1_plants_static, capacityB = task_1_capacityB_static.
```python
from typing import List
def task_1(plants: List[int], val_1: int, capacityB: int) -> int:
    (a, b) = (val_1, capacityB)
    ans = 0
    (i, j) = (0, len(plants) - 1)
    while i < j:
        if a < plants[i]:
            ans += 1
            a = val_1
        a -= plants[i]
        if b < plants[j]:
            ans += 1
            b = capacityB
        b -= plants[j]
        (i, j) = (i + 1, j - 1)
    ans += i == j and max(a, b) < plants[i]
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -43}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [33, 40, 8, 45, 31, -59, -2, -64, 45, -30].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> int:
    mx = max(nums)
    n = len(nums)
    ans = cnt = j = 0
    for x in nums:
        while j < n and cnt < val_2:
            cnt += nums[j] == mx
            j += 1
        if cnt < val_2:
            break
        ans += n - j + 1
        cnt -= x == mx
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [11, 23, -43, -34, -91, 10, 60, 92, 67, -64]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [7, -19, -13, -1, 46, -13, 34, -32, 5, -72]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    nums = [v - i for (i, v) in enumerate(list_1)]
    n = len(nums)
    left = [-1] * n
    stk = []
    for (i, v) in enumerate(nums):
        while stk and nums[stk[-1]] >= v:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    ans = 0
    dp = [0] * n
    dp[0] = list_1[0]
    for (i, v) in enumerate(list_1):
        j = left[i]
        cnt = min(v, i - j)
        u = v - cnt + 1
        s = (u + v) * cnt // 2
        dp[i] = s + (0 if j == -1 else dp[j])
        ans = max(ans, dp[i])
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 14}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_buses_static = [-84, -58, -51, 78, 67, -39, 1, -68, 73, -20].
Define task_2_passengers_static = [88, 12, 83, -6, 29, 43, 63, 20, 79, 53].
Trace the execution of task_2 with inputs buses = task_2_buses_static, passengers = task_2_passengers_static.
```python
from typing import List
def task_2(buses: List[int], passengers: List[int], val_2: int) -> int:
    buses.sort()
    passengers.sort()
    j = 0
    for t in buses:
        c = val_2
        while c and j < len(passengers) and (passengers[j] <= t):
            (c, j) = (c - 1, j + 1)
    j -= 1
    ans = buses[-1] if c else passengers[j]
    while ~j and passengers[j] == ans:
        (ans, j) = (ans - 1, j - 1)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-53, 88, -7, -71, -15, -83, 19, -19, 33, -41]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 84}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_initialExperience_static = -9.
Define task_1_energy_static = [-15, 61, 75, 18, -79, 93, -60, 44, 68, 18].
Define task_1_experience_static = [-7, -43, -85, -67, -93, -84, -50, 29, -32, 2].
Trace the execution of task_1 with inputs initialExperience = task_1_initialExperience_static, energy = task_1_energy_static, experience = task_1_experience_static.
```python
from typing import List
def task_1(val_1: int, initialExperience: int, energy: List[int], experience: List[int]) -> int:
    sum_energy = sum(energy)
    energy_hours = max(0, sum_energy + 1 - val_1)
    exp_hours = 0
    current_exp = initialExperience
    for e in experience:
        if current_exp <= e:
            delta = e + 1 - current_exp
            exp_hours += delta
            current_exp += delta
        current_exp += e
    python_result_1 = energy_hours + exp_hours
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [16, -66, 40, -57, -87, 97, -63, 48, 36, -85]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_power_static = -81.
Trace the execution of task_2 with inputs power = task_2_power_static.
```python
from typing import List
def task_2(list_2: List[int], power: int) -> int:
    list_2.sort()
    ans = score = 0
    (i, j) = (0, len(list_2) - 1)
    while i <= j:
        if power >= list_2[i]:
            power -= list_2[i]
            (score, i) = (score + 1, i + 1)
            ans = max(ans, score)
        elif score:
            power += list_2[j]
            (score, j) = (score - 1, j - 1)
        else:
            break
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [34, -4, -6, -74, 63, -2, 54, -66, 69, -89]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-20, 14, 35, -13, 11, -31, -5, 62, -100, -51]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Define task_1_queries_static = [-88, 84, -94, -71, 24, -29, 58, -15, 53, -85].
Trace the execution of task_1 with inputs queries = task_1_queries_static.
```python
from typing import List
def task_1(list_1: List[int], queries: List[int]) -> List[int]:
    s = set()
    ans = []
    for q in queries[::-1]:
        if q not in s:
            ans.append(q)
            s.add(q)
    for w in list_1:
        if w not in s:
            ans.append(w)
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 73}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [13, 44, 29, 60, 100, -57, 32, -12, 14, 86].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> int:
    (ans, y) = (1, nums[0])
    for x in nums[1:]:
        if x == 0:
            python_result_2 = 1
            return python_result_2
        if x * y <= val_2:
            y *= x
        else:
            y = x
            ans += 1
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [2, -13, -8, 53, -100, -1, -23, -96, -17, -36]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 82}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_y_static = -71.
Define task_1_bound_static = 96.
Trace the execution of task_1 with inputs y = task_1_y_static, bound = task_1_bound_static.
```python
from typing import List
def task_1(val_1: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_1 == 1:
            break
        a *= val_1
    python_result_1 = list(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 3}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [-87, -41, -56, 91, -46, -72, 83, -25, -21, -11].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-35, -75, 52, -94, -40, -4, 31, 1, -87, -40]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_3)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_3 = (dfs(list_3) - 1 + mod) % mod
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.