```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


_cpp_source = r"""
#include <torch/extension.h>

torch::Tensor shifted_cumsum_cuda(torch::Tensor x);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cub/cub.cuh>

constexpr int THREADS = 256;
constexpr int ITEMS = 8;
constexpr int TILE = THREADS * ITEMS;

__global__ void tile_sums_kernel(
    const float* __restrict__ x,
    float* __restrict__ sums,
    int columns,
    int tiles)
{
    const int tile = blockIdx.x % tiles;
    const int row = blockIdx.x / tiles;
    const int start = tile * TILE;
    const int64_t base = static_cast<int64_t>(row) * columns;

    float sum = 0.0f;
    #pragma unroll
    for (int i = 0; i < ITEMS; ++i) {
        const int column = start + threadIdx.x + i * THREADS;
        if (column < columns)
            sum += x[base + column];
    }

    using Reduce = cub::BlockReduce<float, THREADS>;
    __shared__ typename Reduce::TempStorage storage;
    const float total = Reduce(storage).Sum(sum);

    if (threadIdx.x == 0)
        sums[static_cast<int64_t>(row) * tiles + tile] = total;
}

__global__ void shifted_scan_kernel(
    const float* __restrict__ x,
    const float* __restrict__ sums,
    float* __restrict__ output,
    int columns,
    int tiles)
{
    const int tile = blockIdx.x % tiles;
    const int row = blockIdx.x / tiles;
    const int start = tile * TILE;
    const int remaining = columns - start;
    const int valid = remaining < TILE ? remaining : TILE;

    const int64_t input_base =
        static_cast<int64_t>(row) * columns + start;
    const int64_t output_row =
        static_cast<int64_t>(row) * (static_cast<int64_t>(columns) + 1);

    using Load = cub::BlockLoad<
        float, THREADS, ITEMS, cub::BLOCK_LOAD_WARP_TRANSPOSE>;
    using Scan = cub::BlockScan<float, THREADS>;
    using Store = cub::BlockStore<
        float, THREADS, ITEMS, cub::BLOCK_STORE_WARP_TRANSPOSE>;

    __shared__ union {
        typename Load::TempStorage load;
        typename Scan::TempStorage scan;
        typename Store::TempStorage store;
    } storage;
    __shared__ float carry;

    if (threadIdx.x == 0) {
        float prefix = 0.0f;
        const int64_t sums_base = static_cast<int64_t>(row) * tiles;
        for (int previous = 0; previous < tile; ++previous)
            prefix += sums[sums_base + previous];
        carry = prefix;

        if (tile == 0)
            output[output_row] = 0.0f;
    }

    float values[ITEMS];
    Load(storage.load).Load(x + input_base, values, valid, 0.0f);
    __syncthreads();

    Scan(storage.scan).InclusiveSum(values, values);
    __syncthreads();

    #pragma unroll
    for (int i = 0; i < ITEMS; ++i)
        values[i] += carry;

    Store(storage.store).Store(
        output + output_row + start + 1, values, valid);
}

torch::Tensor shifted_cumsum_cuda(torch::Tensor x)
{
    const c10::cuda::CUDAGuard guard(x.device());

    const int64_t rows = x.size(0) - 1;
    const int columns = static_cast<int>(x.size(1));
    const int tiles = (columns + TILE - 1) / TILE;

    auto output = torch::empty(
        {rows, static_cast<int64_t>(columns) + 1}, x.options());

    if (rows == 0)
        return output;

    auto sums = torch::empty({rows, static_cast<int64_t>(tiles)}, x.options());
    const unsigned int blocks = static_cast<unsigned int>(rows * tiles);
    cudaStream_t stream = at::cuda::getCurrentCUDAStream();

    tile_sums_kernel<<<blocks, THREADS, 0, stream>>>(
        x.data_ptr<float>(), sums.data_ptr<float>(), columns, tiles);
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    shifted_scan_kernel<<<blocks, THREADS, 0, stream>>>(
        x.data_ptr<float>(), sums.data_ptr<float>(),
        output.data_ptr<float>(), columns, tiles);
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    return output;
}
"""

_extension = load_inline(
    name="exclusive_cumsum_tiled_cuda_v1",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["shifted_cumsum_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, dim):
        super().__init__()
        self.dim = dim

    def forward(self, x):
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.ndim == 2
            and self.dim in (1, -1)
            and x.is_contiguous()
            and x.size(0) > 0
            and 0 < x.size(1) <= 1048576
            and (x.size(0) - 1) * ((x.size(1) + 2047) // 2048)
            <= 2147483647
            and not (torch.is_grad_enabled() and x.requires_grad)
        ):
            # Preserve the original [:-1], which slices dimension zero.
            return _extension.shifted_cumsum_cuda(x)

        shifted = torch.cat(
            (
                torch.zeros_like(
                    x.select(self.dim, 0).unsqueeze(self.dim)
                ),
                x,
            ),
            dim=self.dim,
        )[:-1]
        return torch.cumsum(shifted, dim=self.dim)
```